SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Spring (device)</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Spring (device)</span></span>

</h1>

</header>

<p>A <b>spring</b> is a device consisting of an <a href="Elasticity_(physics)" title="Elasticity (physics)">elastic</a> but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed or extended.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Springs can <a href="Energy_storage" title="Energy storage">store energy</a> when compressed. In everyday use, the term most often refers to <a href="Coil_spring" title="Coil spring">coil springs</a>, but there are many different spring designs. Modern springs are typically manufactured from <a href="Spring_steel" title="Spring steel">spring steel</a>. An example of a non-metallic spring is the <a href="Bow_(weapon)" class="mw-redirect" title="Bow (weapon)">bow</a>, made traditionally of flexible <a href="Taxus_baccata" title="Taxus baccata">yew</a> wood, which when <a href="Bow_draw" title="Bow draw">drawn</a> stores energy to propel an <a href="Arrow" title="Arrow">arrow</a>.

</p><p>When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing <a href="Force" title="Force">force</a> approximately proportional to its change in length (this approximation breaks down for larger deflections). The <i>rate</i> or <i>spring constant</i> of a spring is the change in the force it exerts, divided by the change in <a href="Deflection_(engineering)" title="Deflection (engineering)">deflection</a> of the spring. That is, it is the <a href="Gradient" title="Gradient">gradient</a> of the force versus deflection <a href="Curve" title="Curve">curve</a>. An <a href="Tension_(physics)" title="Tension (physics)">extension</a> or <a href="Compression_(physical)" class="mw-redirect" title="Compression (physical)">compression</a> spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in. A <a href="Torsion_spring" title="Torsion spring">torsion spring</a> is a spring that works by twisting; when it is twisted about its axis by an angle, it produces a <a href="Torque" title="Torque">torque</a> proportional to the angle. A torsion spring's rate is in units of torque divided by angle, such as <a href="Newton_metre" class="mw-redirect" title="Newton metre">N·m</a>/<a href="Radian" title="Radian">rad</a> or <a href="Ft%C2%B7lbf" class="mw-redirect" title="Ft·lbf">ft·lbf</a>/degree. The inverse of spring rate is compliance, that is: if a spring has a rate of 10 N/mm, it has a compliance of 0.1 mm/N. The stiffness (or rate) of springs in parallel is <a href="Additive_map" title="Additive map">additive</a>, as is the compliance of springs in series.

</p><p>Springs are made from a variety of elastic materials, the most common being spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from <a href="Annealing_(metallurgy)" class="mw-redirect" title="Annealing (metallurgy)">annealed</a> steel and hardened after manufacture. Some <a href="Non-ferrous_metal" title="Non-ferrous metal">non-ferrous metals</a> are also used, including <a href="Phosphor_bronze" title="Phosphor bronze">phosphor bronze</a> and <a href="Titanium" title="Titanium">titanium</a> for parts requiring corrosion resistance, and low-<a href="Electrical_resistance_and_conductance" title="Electrical resistance and conductance">resistance</a> <a href="Beryllium_copper" title="Beryllium copper">beryllium copper</a> for springs carrying <a href="Electric_current" title="Electric current">electric current</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>Simple non-coiled springs have been used throughout human history, e.g. the <a href="Bow_(weapon)" class="mw-redirect" title="Bow (weapon)">bow</a> (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of <a href="Tweezers" title="Tweezers">tweezers</a> in many cultures. <a href="Ctesibius_of_Alexandria" class="mw-redirect" title="Ctesibius of Alexandria">Ctesibius of Alexandria</a> developed a method for making springs out of an alloy of bronze with an increased proportion of tin, hardened by hammering after it was cast.

</p><p><a href="Coiled_springs" class="mw-redirect" title="Coiled springs">Coiled springs</a> appeared early in the 15th century,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> in door locks.<sup id="cite_ref-White1966_3-0" class="reference"><a href="#cite_note-White1966-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The first spring-powered clocks appeared in that century<sup id="cite_ref-White1966_3-1" class="reference"><a href="#cite_note-White1966-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Rossum1997_5-0" class="reference"><a href="#cite_note-Rossum1997-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and evolved into the first large watches by the 16th century.

</p><p>In 1676 British physicist <a href="Robert_Hooke" title="Robert Hooke">Robert Hooke</a> postulated <a href="Hooke's_law" title="Hooke's law">Hooke's law</a>, which states that the force a spring exerts is proportional to its extension.

</p><p>On March 8, 1850, John Evans, Founder of John Evans' Sons, Incorporated, opened his business in New Haven, Connecticut, manufacturing flat springs for carriages and other vehicles, as well as the machinery to manufacture the springs. Evans was a Welsh blacksmith and springmaker who emigrated to the United States in 1847, John Evans' Sons became "America's oldest springmaker" which continues to operate today.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Classification">Classification</h3></div>

<p>Springs can be classified depending on how the load force is applied to them:

</p>

<dl><dt>Tension/extension spring</dt>

<dd>The spring is designed to operate with a <a href="Tension_(physics)" title="Tension (physics)">tension</a> load, so the spring stretches as the load is applied to it.</dd>

<dt>Compression spring</dt>

<dd>Designed to operate with a compression load, so the spring gets shorter as the load is applied to it.</dd>

<dt><a href="Torsion_spring" title="Torsion spring">Torsion spring</a></dt>

<dd>Unlike the above types in which the load is an axial force, the load applied to a torsion spring is a <a href="Torque" title="Torque">torque</a> or twisting force, and the end of the spring rotates through an angle as the load is applied.</dd>

<dt>Constant spring</dt>

<dd>Supported load remains the same throughout deflection cycle<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></dd>

<dt>Variable spring</dt>

<dd>Resistance of the coil to load varies during compression<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></dd>

<dt>Variable stiffness spring</dt>

<dd>Resistance of the coil to load can be dynamically varied for example by the control system, some types of these springs also vary their length thereby providing actuation capability as well <sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></dd></dl>

<p>They can also be classified based on their shape:

</p>

<dl><dt>Flat spring</dt>

<dd>Made of a flat <a href="Spring_steel" title="Spring steel">spring steel</a>.</dd>

<dt>Machined spring</dt>

<dd>Manufactured by machining bar stock with a lathe and/or milling operation rather than a coiling operation. Since it is machined, the spring may incorporate features in addition to the elastic element. Machined springs can be made in the typical load cases of compression/extension, torsion, etc.</dd>

<dt>Serpentine spring</dt>

<dd>A zig-zag of thick wire, often used in modern upholstery/furniture.</dd>

<dt><a href="Garter_spring" title="Garter spring">Garter spring</a></dt>

<dd>A coiled steel spring that is connected at each end to create a circular shape.</dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Common_types">Common types</h3></div>

<p>The most common types of spring are:

</p>

<dl><dt>Cantilever spring</dt>

<dd>A flat spring fixed only at one end like a <a href="Cantilever" title="Cantilever">cantilever</a>, while the free-hanging end takes the load.</dd>

<dt><a href="Coil_spring" title="Coil spring">Coil spring</a></dt>

<dd>Also known as a helical spring. A spring (made by winding a wire around a cylinder) is of two types:</dd></dl>

<ul><li><i>Tension</i> or <i>extension springs</i> are designed to become longer under load. Their turns (loops) are normally touching in the unloaded position, and they have a hook, eye or some other means of attachment at each end.</li>

<li><i>Compression springs</i> are designed to become shorter when loaded. Their turns (loops) are not touching in the unloaded position, and they need no attachment points.</li>

<li><i>Hollow tubing springs</i> can be either extension springs or compression springs. Hollow tubing is filled with oil and the means of changing hydrostatic pressure inside the tubing such as a membrane or miniature piston etc. to harden or relax the spring, much like it happens with water pressure inside a garden hose. Alternatively tubing's cross-section is chosen of a shape that it changes its area when tubing is subjected to torsional deformation: change of the cross-section area translates into change of tubing's inside volume and the flow of oil in/out of the spring that can be controlled by valve thereby controlling stiffness. There are many other designs of springs of hollow tubing which can change stiffness with any desired frequency, change stiffness by a multiple or move like a linear actuator in addition to its spring qualities.</li></ul>

<dl><dt><a href="Arc_spring" title="Arc spring">Arc spring</a></dt>

<dd>A pre-curved or arc-shaped helical compression spring, which is able to transmit a torque around an axis.</dd>

<dt><a href="Volute_spring" title="Volute spring">Volute spring</a></dt>

<dd>A compression coil spring in the form of a <a href="Cone_(geometry)" class="mw-redirect" title="Cone (geometry)">cone</a> so that under compression the coils are not forced against each other, thus permitting longer travel.</dd>

<dt><a href="Balance_spring" title="Balance spring">Balance spring</a></dt>

<dd>Also known as a hairspring. A delicate spiral spring used in <a href="Watch" title="Watch">watches</a>, <a href="Galvanometer" title="Galvanometer">galvanometers</a>, and places where electricity must be carried to partially rotating devices such as <a href="Steering_wheel" title="Steering wheel">steering wheels</a> without hindering the rotation.</dd>

<dt><a href="Leaf_spring" title="Leaf spring">Leaf spring</a></dt>

<dd>A flat spring used in vehicle <a href="Suspension_(vehicle)" class="mw-redirect" title="Suspension (vehicle)">suspensions</a>, electrical <a href="Switch" title="Switch">switches</a>, and <a href="Bow_(weapon)" class="mw-redirect" title="Bow (weapon)">bows</a>.</dd>

<dt>V-spring</dt>

<dd>Used in antique <a href="Firearm" title="Firearm">firearm</a> mechanisms such as the <a href="Wheellock" title="Wheellock">wheellock</a>, <a href="Flintlock" title="Flintlock">flintlock</a> and <a href="Percussion_cap" title="Percussion cap">percussion cap</a> locks. Also door-lock spring, as used in antique door latch mechanisms.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Other_types">Other types</h3></div>

<p>Other types include:

</p>

<dl><dt><a href="Belleville_washer" title="Belleville washer">Belleville washer</a></dt>

<dd>A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated <a href="Land_mine" title="Land mine">landmines</a>)</dd>

<dt><a href="Constant-force_spring" title="Constant-force spring">Constant-force spring</a></dt>

<dd>A tightly rolled ribbon that exerts a nearly constant force as it is unrolled</dd>

<dt><a href="Gas_spring" title="Gas spring">Gas spring</a></dt>

<dd>A volume of compressed gas.</dd>

<dt>Ideal spring</dt>

<dd>An idealised perfect spring with no weight, mass, damping losses, or limits, a concept used in physics. The force an ideal spring would exert is exactly proportional to its extension or compression.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></dd>

<dt><a href="Mainspring" title="Mainspring">Mainspring</a></dt>

<dd>A spiral ribbon-shaped spring used as a power store of <a href="Clockwork" title="Clockwork">clockwork</a> mechanisms: <a href="Watch" title="Watch">watches</a>, <a href="Clock" title="Clock">clocks</a>, <a href="Music_box" title="Music box">music boxes</a>, windup <a href="Toy" title="Toy">toys</a>, and <a href="Mechanically_powered_flashlight" title="Mechanically powered flashlight">mechanically powered flashlights</a></dd>

<dt><a href="Constant-force_spring" title="Constant-force spring">Negator spring</a></dt>

<dd>A thin metal band slightly concave in cross-section. When coiled it adopts a flat cross-section but when unrolled it returns to its former curve, thus producing a constant force throughout the displacement and <i>negating</i> any tendency to re-wind. The most common application is the retracting steel tape rule.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></dd>

<dt>Progressive rate coil springs</dt>

<dd>A coil spring with a variable rate, usually achieved by having unequal distance between turns so that as the spring is compressed one or more coils rests against its neighbour.</dd>

<dt><a href="Rubber_band" title="Rubber band">Rubber band</a></dt>

<dd>A tension spring where energy is stored by stretching the material.</dd>

<dt>Spring <a href="Washer_(mechanical)" class="mw-redirect" title="Washer (mechanical)">washer</a></dt>

<dd>Used to apply a constant tensile force along the axis of a <a href="Fastener" title="Fastener">fastener</a>.</dd>

<dt><a href="Torsion_spring" title="Torsion spring">Torsion spring</a></dt>

<dd>Any spring designed to be twisted rather than compressed or extended.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Used in <a href="Torsion_beam_suspension" class="mw-redirect" title="Torsion beam suspension">torsion bar</a> vehicle suspension systems.</dd>

<dt>Wave spring</dt>

<dd>various types of spring made compact by using waves to give a spring effect.</dd></dl>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Wave_spring" title="Wave spring">Wave spring</a></div>

<div class="mw-heading mw-heading2"><h2 id="Physics">Physics</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Hooke's_law">Hooke's law</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Hooke's_law" title="Hooke's law">Hooke's law</a></div>

<p>An ideal spring acts in accordance with Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length:

</p>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F=-kx}</annotation>

</semantics>

</math></span><img src="./aace79ea36db4ebc9f83a00c4198f4c054f5b4fb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.188ex; height:2.343ex;" alt="{\displaystyle F=-kx}" loading="lazy"></span>,</dd></dl>

<p>where

</p>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x}</annotation>

</semantics>

</math></span><img src="./87f9e315fd7e2ba406057a97300593c4802b53e4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" loading="lazy"></span> is the displacement vector – the distance from its equilibrium length.</dd>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F}</annotation>

</semantics>

</math></span><img src="./545fd099af8541605f7ee55f08225526be88ce57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}" loading="lazy"></span> is the resulting force vector – the magnitude and direction of the restoring force the spring exerts</dd>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

</semantics>

</math></span><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> is the <b>rate</b>, <b>spring constant</b> or <b>force constant</b> of the spring, a constant that depends on the spring's material and construction. The negative sign indicates that the force the spring exerts is in the opposite direction from its displacement</dd></dl>

<p>Most real springs approximately follow Hooke's law if not stretched or compressed beyond their <a href="Elastic_limit" class="mw-redirect" title="Elastic limit">elastic limit</a>.

</p><p>Coil springs and other common springs typically obey Hooke's law. There are useful springs that don't: springs based on beam bending can for example produce forces that vary <a href="Nonlinear" class="mw-redirect" title="Nonlinear">nonlinearly</a> with displacement.

</p><p>If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.

</p>

<div class="mw-heading mw-heading3"><h3 id="Simple_harmonic_motion">Simple harmonic motion</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Harmonic_oscillator" title="Harmonic oscillator">Harmonic oscillator</a></div>

<p>Since force is equal to mass, <i>m</i>, times acceleration, <i>a</i>, the force equation for a spring obeying Hooke's law looks like:

</p>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,}</annotation>

</semantics>

</math></span><img src="./73a7f5f50293d7430c10e80ed069351b0714c382.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:28.12ex; height:2.343ex;" alt="{\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,}" loading="lazy"></span></dd></dl>

<p>The mass of the spring is small in comparison to the mass of the attached mass and is ignored. Since acceleration is simply the second <a href="Derivative" title="Derivative">derivative</a> of x with respect to time,

</p>

<mfrac>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle -kx=m{\frac {d^{2}x}{dt^{2}}}.\,}</annotation>

</semantics>

</math></span><img src="./b17214b733b2168a7f015a7e789ea8e76c777aa5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.96ex; height:6.009ex;" alt="{\displaystyle -kx=m{\frac {d^{2}x}{dt^{2}}}.\,}" loading="lazy"></span></dd></dl>

<p>This is a second order linear <a href="Differential_equation" title="Differential equation">differential equation</a> for the displacement <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x}</annotation>

</semantics>

</p>

<mfrac>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

<mfrac>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0,\,}</annotation>

</semantics>

</math></span><img src="./d3be5f7951c51deec26ef404594d49168510ad14.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.78ex; height:6.009ex;" alt="{\displaystyle {\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0,\,}" loading="lazy"></span></dd></dl>

<p>the solution of which is the sum of a <a href="Sine" class="mw-redirect" title="Sine">sine</a> and <a href="Cosine" class="mw-redirect" title="Cosine">cosine</a>:

</p>

<mrow>

<mrow>

<msqrt>

<mfrac>

</mfrac>

</msqrt>

</mrow>

</mrow>

<mrow>

<mrow>

<msqrt>

<mfrac>

</mfrac>

</msqrt>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x(t)=A\sin \left(t{\sqrt {\frac {k}{m}}}\right)+B\cos \left(t{\sqrt {\frac {k}{m}}}\right).\,}</annotation>

</semantics>

</math></span><img src="./98cdfcd3c187a0503f1bdf7830121fe675173dcc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.122ex; height:6.343ex;" alt="{\displaystyle x(t)=A\sin \left(t{\sqrt {\frac {k}{m}}}\right)+B\cos \left(t{\sqrt {\frac {k}{m}}}\right).\,}" loading="lazy"></span></dd></dl>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span> are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B=0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B=0}</annotation>

</semantics>

</math></span><img src="./af1d79a64f775646f76d79a452ca8e1082fb1f17.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.025ex; height:2.176ex;" alt="{\displaystyle B=0}" loading="lazy"></span> (zero initial position with some positive initial velocity) is displayed in the image on the right.

</p>

<div class="mw-heading mw-heading3"><h3 id="Energy_dynamics">Energy dynamics</h3></div>

<p>In <a href="Simple_harmonic_motion" title="Simple harmonic motion">simple harmonic motion</a> of a spring-mass system, energy will fluctuate between <a href="Kinetic_energy" title="Kinetic energy">kinetic energy</a> and <a href="Potential_energy" title="Potential energy">potential energy</a>, but the total energy of the system remains the same. A spring that obeys <a href="Hooke's_law" title="Hooke's law">Hooke's law</a> with spring constant <i>k</i> will have a total system energy <i>E</i> of:<sup id="cite_ref-:02_14-0" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}}">

<mrow>

<mfrac>

</mfrac>

</mrow>

</mrow>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}}</annotation>

</semantics>

</math></span><img src="./aedd30ca9c7340ecc8c8fc70ea10696a1a8b84fa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.69ex; height:6.176ex;" alt="{\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}}" loading="lazy"></span>

</p><p>Here, A is the <a href="Amplitude" title="Amplitude">amplitude</a> of the wave-like motion that is produced by the oscillating behavior of the spring.

</p><p>The potential energy <i>U</i> of such a system can be determined through the spring constant <i>k</i> and its displacement <i>x</i>:<sup id="cite_ref-:02_14-1" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

<mrow>

<mfrac>

</mfrac>

</mrow>

</mrow>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}}</annotation>

</semantics>

</math></span><img src="./d2059b1fb3dcfefff43dbdf3416fa07cd11a6696.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.283ex; height:6.176ex;" alt="{\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}}" loading="lazy"></span>

</p><p>The <a href="Kinetic_energy" title="Kinetic energy">kinetic energy</a> <i>K</i> of an object in <a href="Simple_harmonic_motion" title="Simple harmonic motion">simple harmonic motion</a> can be found using the mass of the attached object <i>m</i> and the <a href="Velocity" title="Velocity">velocity</a> at which the object oscillates <i>v</i>:<sup id="cite_ref-:02_14-2" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

<mrow>

<mfrac>

</mfrac>

</mrow>

</mrow>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle K=\left({\frac {1}{2}}\right)mv^{2}}</annotation>

</semantics>

</math></span><img src="./9a98325b25abab252bd5f844a514647a528f2786.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.194ex; height:6.176ex;" alt="{\displaystyle K=\left({\frac {1}{2}}\right)mv^{2}}" loading="lazy"></span>

</p><p>Since there is no energy loss in such a system, energy is always conserved and thus:<sup id="cite_ref-:02_14-3" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E=K+U}</annotation>

</semantics>

</math></span><img src="./734f872b98d17048701d0310b6fa05e0c7518c4a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.563ex; height:2.343ex;" alt="{\displaystyle E=K+U}" loading="lazy"></span>

</p>

<div class="mw-heading mw-heading3"><h3 id="Frequency_&_period">Frequency & period</h3></div>

<p>The <a href="Angular_frequency" title="Angular frequency">angular frequency</a> ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant <i>k</i> and the mass of the oscillating object <i>m</i><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><i>:</i>

<msqrt>

<mfrac>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \omega ={\sqrt {\frac {k}{m}}}}</annotation>

</semantics>

</math></span><img src="./e901183c61a98d7f3f967c78f7ec02c0f0507be5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.745ex; height:6.176ex;" alt="{\displaystyle \omega ={\sqrt {\frac {k}{m}}}}" loading="lazy"></span><sup id="cite_ref-:02_14-4" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p><p>The period <i>T</i>, the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by:<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msqrt>

<mfrac>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {m}{k}}}}</annotation>

</semantics>

</math></span><img src="./b940babc687351ce45b92fafd283d3981a34bab6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:18.859ex; height:6.176ex;" alt="{\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {m}{k}}}}" loading="lazy"></span><sup id="cite_ref-:02_14-5" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p><p>The <a href="Frequency" title="Frequency">frequency</a> <i>f</i>, the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period:<sup id="cite_ref-:02_14-6" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

<mfrac>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msqrt>

<mfrac>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f={\frac {1}{T}}={\frac {\omega }{2\pi }}={\frac {1}{2\pi }}{\sqrt {\frac {k}{m}}}}</annotation>

</semantics>

</math></span><img src="./880bd6f1fa6d999ee15070cf294fae56bc7eb133.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.908ex; height:6.176ex;" alt="{\displaystyle f={\frac {1}{T}}={\frac {\omega }{2\pi }}={\frac {1}{2\pi }}{\sqrt {\frac {k}{m}}}}" loading="lazy"></span><sup id="cite_ref-:02_14-7" class="reference"><a href="#cite_note-:02-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2></div>

<p>In <a href="Classical_physics" title="Classical physics">classical physics</a>, a spring can be seen as a device that stores <a href="Potential_energy" title="Potential energy">potential energy</a>, specifically <a href="Elastic_potential_energy" class="mw-redirect" title="Elastic potential energy">elastic potential energy</a>, by straining the bonds between the <a href="Atom" title="Atom">atoms</a> of an <a href="Elasticity_(physics)" title="Elasticity (physics)">elastic</a> material.

</p><p>Hooke's law of <a href="Theory_of_elasticity" class="mw-redirect" title="Theory of elasticity">elasticity</a> states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its <a href="Tension_(mechanics)" class="mw-redirect" title="Tension (mechanics)">tension</a>, the <a href="Force" title="Force">force</a> used to stretch it. Similarly, the contraction (negative extension) is proportional to the <a href="Compression_(physical)" class="mw-redirect" title="Compression (physical)">compression</a> (negative tension).

</p><p>This law actually holds only approximately, and only when the deformation (extension or contraction) is small compared to the rod's overall length. For deformations beyond the <a href="Tensile_strength" class="mw-redirect" title="Tensile strength">elastic limit</a>, atomic bonds get broken or rearranged, and a spring may snap, buckle, or permanently deform. Many materials have no clearly defined elastic limit, and Hooke's law can not be meaningfully applied to these materials. Moreover, for the superelastic materials, the linear relationship between force and displacement is appropriate only in the low-strain region.

</p><p>Hooke's law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. Any <a href="Smooth_function" class="mw-redirect" title="Smooth function">smooth function</a> of one variable approximates a <a href="Quadratic_function" title="Quadratic function">quadratic function</a> when examined near enough to its minimum point as can be seen by examining the <a href="Taylor_series" title="Taylor series">Taylor series</a>. Therefore, the force – which is the derivative of energy with respect to displacement – approximates a <a href="Linear_function" title="Linear function">linear function</a>.

</p><p>The force of a fully compressed spring is:

</p>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F_{max}={\frac {Ed^{4}(L-nd)}{16(1+\nu )(D-d)^{3}n}}\ }</annotation>

</semantics>

</math></span><img src="./7eddc31f2c75425aec01b08159d26faa56277219.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:29.103ex; height:6.676ex;" alt="{\displaystyle F_{max}={\frac {Ed^{4}(L-nd)}{16(1+\nu )(D-d)^{3}n}}\ }" loading="lazy"></span></dd></dl>

<p>where

</p>

<dl><dd>E – <a href="Young's_modulus" title="Young's modulus">Young's modulus</a></dd>

<dd>d – spring wire diameter</dd>

<dd>L – free length of spring</dd>

<dd>n – number of active windings</dd>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \nu }</annotation>

</semantics>

</math></span><img src="./c15bbbb971240cf328aba572178f091684585468.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }" loading="lazy"></span> – <a href="Poisson_ratio" class="mw-redirect" title="Poisson ratio">Poisson ratio</a></dd>

<dd>D – spring outer diameter.</dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Zero-length_springs">Zero-length springs</h2></div>

<p><b>Zero-length spring</b> is a term for a specially designed coil spring that would exert zero force if it had zero length. That is, in a line graph of the spring's force versus its length, the line passes through the origin. A real coil spring will not contract to zero length because at some point the coils touch each other. "Length" here is defined as the distance between the axes of the pivots at each end of the spring, regardless of any inelastic portion in-between.

</p><p>Zero-length springs are made by manufacturing a coil spring with built-in tension (A twist is introduced into the wire as it is coiled during manufacture; this works because a coiled spring <i>unwinds</i> as it stretches), so if it <i>could</i> contract further, the equilibrium point of the spring, the point at which its restoring force is zero, occurs at a length of zero. In practice, the manufacture of springs is typically not accurate enough to produce springs with tension consistent enough for applications that use zero length springs, so they are made by combining a <i>negative length</i> spring, made with even more tension so its equilibrium point would be at a <i>negative</i> length, with a piece of inelastic material of the proper length so the zero force point would occur at zero length.

</p><p>

A zero-length spring can be attached to a mass on a hinged boom in such a way that the force on the mass is almost exactly balanced by the vertical component of the force from the spring, whatever the position of the boom. This creates a horizontal pendulum with very long oscillation <a href="Period_(physics)" class="mw-redirect" title="Period (physics)">period</a>. Long-period pendulums enable <a href="Seismometer" title="Seismometer">seismometers</a> to sense the slowest waves from earthquakes. The <a href="Lucien_LaCoste" title="Lucien LaCoste">LaCoste</a> suspension with zero-length springs is also used in <a href="Gravimeter" class="mw-redirect" title="Gravimeter">gravimeters</a> because it is very sensitive to changes in gravity. Springs for closing doors are often made to have roughly zero length, so that they exert force even when the door is almost closed, so they can hold it closed firmly.</p><div style="clear:left;" class=""></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}

/* end https://en.wikipedia.org/ */

</style><div class="div-col">

<ul><li><a href="Airsoft_gun" title="Airsoft gun">Airsoft gun</a></li>

<li><a href="Aerospace" title="Aerospace">Aerospace</a></li>

<li>Retractable <a href="Ballpoint_pen" title="Ballpoint pen">ballpoint pens</a></li>

<li><a href="Buckling_spring" title="Buckling spring">Buckling spring</a> keyboards</li>

<li><a href="Clockwork" title="Clockwork">Clockwork</a> clocks, watches, and other things</li>

<li><a href="Firearms" class="mw-redirect" title="Firearms">Firearms</a></li>

<li>Forward or aft spring, a method of <a href="Mooring#Mooring_to_a_shore_fixture" title="Mooring">mooring</a> a vessel to a shore fixture</li>

<li><a href="Gravimeter" class="mw-redirect" title="Gravimeter">Gravimeters</a></li>

<li>Industrial Equipment</li>

<li><a href="Jewelry" class="mw-redirect" title="Jewelry">Jewelry</a>: Clasp mechanisms</li>

<li>Most <a href="Folding_knife" class="mw-redirect" title="Folding knife">folding knives</a>, and <a href="Switchblade" title="Switchblade">switchblades</a></li>

<li><a href="Lock_(security_device)" class="mw-redirect" title="Lock (security device)">Lock</a> mechanisms: Key-recognition and for coordinating the movements of various parts of the lock.</li>

<li><a href="Mattress" title="Mattress">Spring mattresses</a></li>

<li><a href="Medical_device" title="Medical device">Medical Devices</a><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Pogo_Stick" class="mw-redirect" title="Pogo Stick">Pogo Stick</a></li>

<li>Pop-open devices: <a href="CD_player" title="CD player">CD players</a>, <a href="Tape_recorder" title="Tape recorder">tape recorders</a>, <a href="Toaster" title="Toaster">toasters</a>, etc.</li>

<li><a href="Reverb_effect#Spring_reverb" title="Reverb effect">Spring reverb</a></li>

<li><a href="Toy" title="Toy">Toys</a>; the <a href="Slinky" title="Slinky">Slinky</a> toy is just a spring</li>

<li><a href="Trampoline" title="Trampoline">Trampoline</a></li>

<li><a href="Upholstery_coil_springs" title="Upholstery coil springs">Upholstery coil springs</a></li>

<li><a href="Vehicle_suspension" class="mw-redirect" title="Vehicle suspension">Vehicle suspension</a>, <a href="Leaf_springs" class="mw-redirect" title="Leaf springs">Leaf springs</a></li></ul>

</div>

<ul><li><a href="Shock_absorber" title="Shock absorber">Shock absorber</a></li>

<li><a href="Slinky" title="Slinky">Slinky</a>, helical spring toy</li>

<li><a href="Volute_spring" title="Volute spring">Volute spring</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}

/* end https://en.wikipedia.org/ */

</style><div class="reflist">

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFReference-OED-spring" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/view/Entry/187725">"spring"</a></span>. <i><a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span> V. 25.</span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.madehow.com/Volume-6/Springs.html">Springs</a> How Products Are Made, 14 July 2007.</span>

</li>

<li id="cite_note-White1966-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-White1966_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-White1966_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFWhite1966" class="citation book cs1">White, Lynn Jr. (1966). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/medievaltechnolo00whit"><i>Medieval Technology and Social Change</i></a></span>. New York: Oxford Univ. Press. pp. <span class="nowrap">126–</span>27. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-500266-0</bdi>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFUsher1988" class="citation book cs1">Usher, Abbot Payson (1988). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xuDDqqa8FlwC&pg=PA305"><i>A History of Mechanical Inventions</i></a>. Courier Dover. p. 305. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-486-25593-X</bdi>.</cite></span>

</li>

<li id="cite_note-Rossum1997-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rossum1997_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFDohrn-van_Rossum1998" class="citation book cs1">Dohrn-van Rossum, Gerhard (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=53K32RiEigMC&pg=PA121"><i>History of the Hour: Clocks and Modern Temporal Orders</i></a>. Univ. of Chicago Press. p. 121. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-226-15510-2</bdi>.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFFawcett1983" class="citation cs2">Fawcett, W. Peyton (1983), <a rel="nofollow" class="external text" href="https://www.americanabookstore.com/pages/books/20947/w-peyton-fawcet/history-of-the-spring-industry-in-the-united-states-and-canada"><i>History of the Spring Industry</i></a>, Spring Manufacturers Institute, Inc., p. 28</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.pipingtech.com/products/constant-springs.htm">Constant Springs</a> Piping Technology and Products, (retrieved March 2012)</span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.pipingtech.com/products/variable-springs.htm">Variable Spring Supports</a> Piping Technology and Products, (retrieved March 2012)</span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://patents.google.com/patent/WO2017077541A9/en">"Springs with dynamically variable stiffness and actuation capability"</a>. 3 November 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">20 March</span> 2018</span> – via google.com.</cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{cite journal}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (help)</span></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.springmasters.com/sp/door-lock-springs.html">"Door Lock Springs"</a>. <i>www.springmasters.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 March</span> 2018</span>.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFEdwards2017" class="citation audio-visual cs1">Edwards, Boyd F. (27 October 2017). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=zoGL52P5VWo"><i>The Ideal Spring and Simple Harmonic Motion</i></a> <span class="cs1-format">(Video)</span>. Utah State University – via YouTube.</cite> Based on <cite id="CITEREFCutnellJohnsonYoungStadler2015" class="citation book cs1">Cutnell, John D.; Johnson, Kenneth W.; Young, David; Stadler, Shane (2015). "10.1 The Ideal Spring and Simple Harmonic Motion". <i>Physics</i>. Hoboken, NJ: Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-118-48689-4</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/892304999">892304999</a>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFSamuelWeir,_John1999" class="citation book cs1">Samuel, Andrew; Weir, John (1999). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoen00samu"><i>Introduction to engineering design: modelling, synthesis and problem solving strategies</i></a></span> (2 ed.). Oxford, England: Butterworth. p. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoen00samu/page/n138">134</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7506-4282-3</bdi>.</cite></span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFGoetsch2005" class="citation book cs1">Goetsch, David L. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eMqVygLDSa0C&pg=PA577"><i>Technical Drawing</i></a>. Cengage Learning. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>1-4018-5760-4</bdi>.</cite></span>

</li>

<li id="cite_note-:02-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-:02_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:02_14-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:02_14-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:02_14-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:02_14-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:02_14-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:02_14-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:02_14-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/13%3A_Simple_Harmonic_Motion/13.01%3A_The_motion_of_a_spring-mass_system">"13.1: The motion of a spring-mass system"</a>. <i>Physics LibreTexts</i>. 17 September 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">19 April</span> 2021</span>.</cite></span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://labman.phys.utk.edu/phys221core/modules/m11/harmonic_motion.html">"Harmonic motion"</a>. <i>labman.phys.utk.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 April</span> 2021</span>.</cite></span>

</li>

<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/simple-harmonic-motion">"simple harmonic motion | Formula, Examples, & Facts"</a>. <i>Encyclopedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 April</span> 2021</span>.</cite></span>

</li>

<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.coilspringsdirect.com/store/entex-compression-springs">"Compression Springs"</a>. <i>Coil Springs Direct</i>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Sclater, Neil. (2011). "Spring and screw devices and mechanisms." <i>Mechanisms and Mechanical Devices Sourcebook.</i> 5th ed. New York: McGraw Hill. pp. 279–299. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780071704427</bdi>. Drawings and designs of various spring and screw mechanisms.</li>

<li>Parmley, Robert. (2000). "Section 16: Springs." <i>Illustrated Sourcebook of Mechanical Components.</i> New York: McGraw Hill. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0070486174</bdi> Drawings, designs and discussion of various springs and spring mechanisms.</li>

<li>Warden, Tim. (2021). “Bundy 2 Alto Saxophone.” This saxophone is known for having the strongest tensioned needle springs in existence.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .infobox .side-box{font-size:100%}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1237033735">

/* start https://en.wikipedia.org/ */

@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}

/* end https://en.wikipedia.org/ */

</style><div class="side-box side-box-right sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">

/* start https://en.wikipedia.org/ */

.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}

/* end https://en.wikipedia.org/ */

</style>

<div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Spring_(device)" class="extiw external" title="commons:Spring (device)"><span style="font-style:italic; font-weight:bold;">Spring (device)</span></a>.</div></div>

</div>

<ul><li><cite id="CITEREFParedes2013" class="citation web cs1">Paredes, Manuel (2013). <a rel="nofollow" class="external text" href="http://www.meca.insa-toulouse.fr/~paredes/Springs2K/index.php">"How to design springs"</a>. insa de toulouse<span class="reference-accessdate">. Retrieved <span class="nowrap">13 November</span> 2013</span>.</cite></li>

<li><cite id="CITEREFWright" class="citation web cs1">Wright, Douglas. <a rel="nofollow" class="external text" href="http://www.mech.uwa.edu.au/DANotes/springs/intro/intro.html">"Introduction to Springs"</a>. <i>Notes on Design and Analysis of Machine Elements</i>. Department of Mechanical & Material Engineering, <a href="University_of_Western_Australia" title="University of Western Australia">University of Western Australia</a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 February</span> 2008</span>.</cite></li>

<li><cite id="CITEREFSilberstein2002" class="citation web cs1">Silberstein, Dave (2002). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130918155928/http://home.earthlink.net/~bazillion/intro.html">"How to make springs"</a>. Bazillion. Archived from <a rel="nofollow" class="external text" href="https://home.earthlink.net/~bazillion/intro.html">the original</a> on 18 September 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">3 February</span> 2008</span>.</cite></li>

<li><a rel="nofollow" class="external text" href="https://patents.google.com/patent/WO2017077541A9/en">Springs with Dynamically Variable Stiffness (patent)</a></li>

<li><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US20170051808A1/en">Smart Springs and their Combinations (patent)</a></li></ul>

</p>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1236075235">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Machines359" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div id="Machines359" style="font-size:114%;margin:0 4em"><a href="Machine" title="Machine">Machines</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Simple_machine" title="Simple machine">Classical simple machines</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Inclined_plane" title="Inclined plane">Inclined plane</a></li>

<li><a href="Lever" title="Lever">Lever</a></li>

<li><a href="Pulley" title="Pulley">Pulley</a></li>

<li><a href="Screw_(simple_machine)" class="mw-redirect" title="Screw (simple machine)">Screw</a></li>

<li><a href="Wedge_(mechanical_device)" class="mw-redirect" title="Wedge (mechanical device)">Wedge</a></li>

<li><a href="Wheel_and_axle" title="Wheel and axle">Wheel and axle</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Clock" title="Clock">Clocks</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Atomic_clock" title="Atomic clock">Atomic clock</a></li>

<li><a href="Marine_chronometer" title="Marine chronometer">Chronometer</a></li>

<li><a href="Pendulum_clock" title="Pendulum clock">Pendulum clock</a></li>

<li><a href="Quartz_clock" title="Quartz clock">Quartz clock</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Gas_compressor" class="mw-redirect" title="Gas compressor">Compressors</a> and <a href="Pump" title="Pump">pumps</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Archimedes'_screw" title="Archimedes' screw">Archimedes' screw</a></li>

<li><a href="Injector" title="Injector">Eductor-jet pump</a></li>

<li><a href="Hydraulic_ram" title="Hydraulic ram">Hydraulic ram</a></li>

<li><a href="Trompe" title="Trompe">Trompe</a></li>

<li><a href="Vacuum_pump" title="Vacuum pump">Vacuum pump</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="External_combustion_engine" title="External combustion engine">External combustion engines</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Steam_engine" title="Steam engine">Steam engine</a></li>

<li><a href="Stirling_engine" title="Stirling engine">Stirling engine</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Internal_combustion_engine" title="Internal combustion engine">Internal combustion engines</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gas_turbine" title="Gas turbine">Gas turbine</a></li>

<li><a href="Reciprocating_engine" title="Reciprocating engine">Reciprocating engine</a></li>

<li><a href="Rotary_engine" title="Rotary engine">Rotary engine</a></li>

<li><a href="Nutating_disc_engine" title="Nutating disc engine">Nutating disc engine</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linkage_(mechanical)" title="Linkage (mechanical)">Linkages</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Pantograph" title="Pantograph">Pantograph</a></li>

<li><a href="Peaucellier%E2%80%93Lipkin_linkage" title="Peaucellier–Lipkin linkage">Peaucellier-Lipkin</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Turbine" title="Turbine">Turbine</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gas_turbine" title="Gas turbine">Gas turbine</a></li>

<li><a href="Jet_engine" title="Jet engine">Jet engine</a></li>

<li><a href="Steam_turbine" title="Steam turbine">Steam turbine</a></li>

<li><a href="Water_turbine" title="Water turbine">Water turbine</a></li>

<li><a href="Wind_generator" class="mw-redirect" title="Wind generator">Wind generator</a></li>

<li><a href="Windmill" title="Windmill">Windmill</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Airfoil" title="Airfoil">Aerofoil</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Rudder" title="Rudder">Rudder</a></li>

<li><a href="Propeller_(aircraft)" class="mw-redirect" title="Propeller (aircraft)">Propeller</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Electronics" title="Electronics">Electronics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Vacuum_tube" title="Vacuum tube">Vacuum tube</a></li>

<li><a href="Transistor" title="Transistor">Transistor</a></li>

<li><a href="Diode" title="Diode">Diode</a></li>

<li><a href="Resistor" title="Resistor">Resistor</a></li>

<li><a href="Capacitor" title="Capacitor">Capacitor</a></li>

<li><a href="Inductor" title="Inductor">Inductor</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Vehicle" title="Vehicle">Vehicles</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Automobile" class="mw-redirect" title="Automobile">Automobile</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mecha" title="Mecha">Mecha</a></li>

<li><a href="Robot" title="Robot">Robot</a></li>

<li><a href="List_of_agricultural_machinery" title="List of agricultural machinery">Agricultural</a></li>

<li><a href="Seed-counting_machine" title="Seed-counting machine">Seed-counting machine</a></li>

<li><a href="Vending_machine" title="Vending machine">Vending machine</a></li>

<li><a href="Wind_tunnel" title="Wind tunnel">Wind tunnel</a></li>

<li><a href="Check_weigher" title="Check weigher">Check weighing machines</a></li>

<li><a href="Riveting_machines" class="mw-redirect" title="Riveting machines">Riveting machines</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Springs</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr></tbody></table></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q102836#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1361" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q102836#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1361" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.worldcat.org/fast/1130943">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4016583-8">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85127022">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12286723g">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12286723g">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00560505">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="pružiny"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph249492&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007529683305171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/f74031a4-43b0-4511-9d7b-c1e0cce8b314">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-07-29" href="https://en.wikipedia.org/wiki/?title=Spring_(device)&oldid=1303223653">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>