# Spring (device) > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Spring_(device) > Markdown URL: https://mediated.wiki/source/Spring_(device).md > Source: https://en.wikipedia.org/wiki/Spring_(device) > Source revision: 1348725769 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Elastic object that stores mechanical energy Force (F) vs extension (s).[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] Spring characteristics: (1) progressive, (2) linear, (3) degressive, (4) almost constant, (5) progressive with knee A machined spring incorporates several features into one piece of bar stock Battery contacts often have a variable spring A **spring** is a device consisting of an [elastic](/source/Elasticity_(physics)) but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed, extended or twisted.[1] Springs can [store energy](/source/Energy_storage) when compressed, when extended, and/or when twisted. In everyday use, the term most often refers to [coil springs](/source/Coil_spring), but there are many different spring designs. Modern springs are typically manufactured from [spring steel](/source/Spring_steel). An example of a non-metallic spring is the [bow](/source/Bow_(weapon)), made traditionally of flexible [yew](/source/Taxus_baccata) wood, which when [drawn](/source/Bow_draw) stores energy to propel an [arrow](/source/Arrow). When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing [force](/source/Force) approximately proportional to its change in length (this approximation breaks down for larger deflections). The *rate* or *spring constant* of a spring is the change in the force it exerts, divided by the change in [deflection](/source/Deflection_(engineering)) of the spring. That is, it is the [gradient](/source/Gradient) of the force versus deflection [curve](/source/Curve). An [extension](/source/Tension_(physics)) or [compression](/source/Compression_(physical)) spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in. A [torsion spring](/source/Torsion_spring) is a spring that works by twisting; when it is twisted about its axis by an angle, it produces a [torque](/source/Torque) proportional to the angle. A torsion spring's rate is in units of torque divided by angle, such as [N·m](/source/Newton_metre)/[rad](/source/Radian) or [ft·lbf](/source/Ft%C2%B7lbf)/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 [additive](/source/Additive_map), as is the compliance of springs in series. 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 [annealed](/source/Annealing_(metallurgy)) steel and hardened after manufacture. Some [non-ferrous metals](/source/Non-ferrous_metal) are also used, including [phosphor bronze](/source/Phosphor_bronze) and [titanium](/source/Titanium) for parts requiring corrosion resistance, and low-[resistance](/source/Electrical_resistance_and_conductance) [beryllium copper](/source/Beryllium_copper) for springs carrying [electric current](/source/Electric_current). ## History Simple non-coiled springs have been used throughout human history, e.g. the [bow](/source/Bow_(weapon)) (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of [tweezers](/source/Tweezers) in many cultures. [Ctesibius of Alexandria](/source/Ctesibius_of_Alexandria) 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. [Coiled springs](/source/Coiled_springs) appeared early in the 15th century,[2] in door locks.[3] The first spring-powered clocks appeared in that century[3][4][5] and evolved into the first large watches by the 16th century. In 1676 British physicist [Robert Hooke](/source/Robert_Hooke) postulated [Hooke's law](/source/Hooke's_law), which states that the force a spring exerts is proportional to its extension. 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.[6] ## Types ### Classification Different ways to apply a load force. Springs can be classified depending on how the load force is applied to them. **Tension/extension spring** - The spring is designed to operate with a [tension](/source/Tension_(physics)) load, so the spring stretches as the load is applied to it. [Helical](/source/Helix) [coil springs](/source/Coil_spring) designed for tension. Tension springs in a folded line reverberation device. **Compression spring** - Designed to operate with a [compression](/source/Compression_(physics)) load, so the spring gets shorter as the load is applied to it. **[Torsion spring](/source/Torsion_spring)** - Unlike the above types in which the load is an axial force, the load applied to a torsion spring is a [torque](/source/Torque) or twisting force, and the end of the spring rotates through an angle as the load is applied.[7] Often used in [torsion bar](/source/Torsion_beam_suspension) vehicle suspension systems. A torsion bar twisted under load There are many other ways to potentially classify and subclassify springs, such as their shape - [coil springs](/source/Coil_spring) are common, but so are [leaf springs](/source/Leaf_spring), for example. [Garter springs](/source/Garter_spring) are [arc springs](/source/Arc_spring) with a specific arc in mind; both are typically made by bending a coil spring into a position. ### Common types The most common types of spring are: **[Balance spring](/source/Balance_spring)** - Also known as a hairspring. A delicate spiral spring used in [watches](/source/Watch), [galvanometers](/source/Galvanometer), and places where electricity must be carried to partially rotating devices such as [steering wheels](/source/Steering_wheel) without hindering the rotation. **Cantilever spring** - A flat spring fixed only at one end like a [cantilever](/source/Cantilever), while the free-hanging end takes the load. **[Coil spring](/source/Coil_spring)** - Also known as a helical spring. A spring (made by winding a wire around a cylinder) is of two types. - *Tension* or *extension springs* 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. - *Compression springs* are designed to become shorter when loaded. Their turns (loops) are not touching in the unloaded position, and they need no attachment points. **[Arc spring](/source/Arc_spring)** - A pre-curved or arc-shaped helical (coiled) compression spring, which is able to transmit a torque around an axis. **[Garter spring](/source/Garter_spring)** - An arc spring where the arc is a full circle. They can be compression or extension springs. **[Volute spring](/source/Volute_spring) A [volute spring](/source/Volute_spring). Under compression the coils slide over each other to afford longer travel. Vertical volute springs of a [Stuart tank](/source/Stuart_tank)** - A coil spring in the form of a [cone](/source/Cone_(geometry)) so that under compression the coils are not forced against each other, thus permitting longer travel. **[Hollow tubing spring](/source/Hydrospring)** - 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. **[Leaf spring](/source/Leaf_spring)** - A flat spring used in vehicle [suspensions](/source/Suspension_(vehicle)), electrical [switches](/source/Switch), and [bows](/source/Bow_(weapon)). **V-spring** - Also known as Chevron spring.[8][9] Used in antique [firearm](/source/Firearm) mechanisms such as the [wheellock](/source/Wheellock), [flintlock](/source/Flintlock) and [percussion cap](/source/Percussion_cap) locks. Also used as a door-lock spring, such as in antique door latch mechanisms.[10][*[failed verification](https://en.wikipedia.org/wiki/Wikipedia:Verifiability)*] - A spiral torsion spring, or [hairspring](/source/Hairspring), in an [alarm clock](/source/Alarm_clock). - A heavy-duty coil spring designed for compression and tension - The [English longbow](/source/English_longbow) – a simple but very powerful spring made of [yew](/source/European_Yew), measuring 2 m (6 ft 7 in) long, with a 470 N (105 lbf) [draw weight](/source/Draw_weight), with each limb functionally a [cantilever](/source/Cantilever) spring and the entire bow acting as an extension [arc spring](/source/Arc_spring). - Selection of various [arc springs](/source/Arc_spring) and arc spring systems (systems consisting of inner and outer arc springs). - [Leaf spring](/source/Leaf_spring) on a truck ### Other types Other types include: **[Belleville washer](/source/Belleville_washer)** - A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated [landmines](/source/Land_mine)) **[Constant-force spring](/source/Constant-force_spring)** - A tightly rolled ribbon that exerts a nearly constant force as it is unrolled **[Gas spring](/source/Gas_spring)** - A volume of compressed gas. **Ideal spring** - 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.[11] **[Mainspring](/source/Mainspring)** - A spiral ribbon-shaped spring used as a power store of [clockwork](/source/Clockwork) mechanisms: [watches](/source/Watch), [clocks](/source/Clock), [music boxes](/source/Music_box), windup [toys](/source/Toy), and [mechanically powered flashlights](/source/Mechanically_powered_flashlight) **[Negator spring](/source/Constant-force_spring)** - 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 *negating* any tendency to re-wind. The most common application is the retracting steel tape rule.[12] **Progressive rate coil springs** - 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. **[Rubber band](/source/Rubber_band)** - A tension spring where energy is stored by stretching the material. **Spring [washer](/source/Washer_(mechanical))** - Used to apply a constant tensile force along the axis of a [fastener](/source/Fastener). **Wave spring** - various types of spring made compact by using waves to give a spring effect. Main article: [Wave spring](/source/Wave_spring) ## Physics ### Hooke's law Main article: [Hooke's law](/source/Hooke's_law) 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: F = − k x {\displaystyle F=-kx} where - x is the displacement vector – the distance from its equilibrium length. - F is the resulting force vector – the magnitude and direction of the restoring force the spring exerts - k is the **rate**, **spring constant** or **force constant** 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 Most real springs approximately follow Hooke's law if not stretched or compressed beyond their [elastic limit](/source/Elastic_limit). 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 [nonlinearly](/source/Nonlinear) with displacement. If made with constant pitch (wire thickness), [conical springs](https://en.wikipedia.org/w/index.php?title=Conical_springs&action=edit&redlink=1) 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. ### Simple harmonic motion Main article: [Harmonic oscillator](/source/Harmonic_oscillator) Since force is equal to mass, *m*, times acceleration, *a*, the force equation for a spring obeying 's law looks like: - F = m a ⇒ − k x = m a . {\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,} The displacement, *x*, as a function of time. The amount of time that passes between peaks is called the [period](/source/Wave_period). 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 [derivative](/source/Derivative) of x with respect to time, - − k x = m d 2 x d t 2 . {\displaystyle -kx=m{\frac {d^{2}x}{dt^{2}}}.\,} This is a second order linear [differential equation](/source/Differential_equation) for the displacement x {\displaystyle x} as a function of time. Rearranging: - d 2 x d t 2 + k m x = 0 , {\displaystyle {\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0,\,} the solution of which is the sum of a [sine](/source/Sine) and [cosine](/source/Cosine): - x ( t ) = A sin ⁡ ( t k m ) + B cos ⁡ ( t k m ) . {\displaystyle x(t)=A\sin \left(t{\sqrt {\frac {k}{m}}}\right)+B\cos \left(t{\sqrt {\frac {k}{m}}}\right).\,} A {\displaystyle A} and B {\displaystyle B} are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with B = 0 {\displaystyle B=0} (zero initial position with some positive initial velocity) is displayed in the image on the right. ### Energy dynamics In [simple harmonic motion](/source/Simple_harmonic_motion) of a spring-mass system, energy will fluctuate between [kinetic energy](/source/Kinetic_energy) and [potential energy](/source/Potential_energy), but the total energy of the system remains the same. A spring that obeys [Hooke's law](/source/Hooke's_law) with spring constant *k* will have a total system energy *E* of:[13] E = ( 1 2 ) k A 2 {\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}} Here, A is the [amplitude](/source/Amplitude) of the wave-like motion that is produced by the oscillating behavior of the spring. The potential energy *U* of such a system can be determined through the spring constant *k* and its displacement *x*:[13] U = ( 1 2 ) k x 2 {\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}} The [kinetic energy](/source/Kinetic_energy) *K* of an object in [simple harmonic motion](/source/Simple_harmonic_motion) can be found using the mass of the attached object *m* and the [velocity](/source/Velocity) at which the object oscillates *v*:[13] K = ( 1 2 ) m v 2 {\displaystyle K=\left({\frac {1}{2}}\right)mv^{2}} Since there is no energy loss in such a system, energy is always conserved and thus:[13] E = K + U {\displaystyle E=K+U} ### Frequency & period The [angular frequency](/source/Angular_frequency) ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant *k* and the mass of the oscillating object *m*:[14][13] ω = k m {\displaystyle \omega ={\sqrt {\frac {k}{m}}}} The period *T*, the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by:[15][13] T = 2 π ω = 2 π m k {\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {m}{k}}}} The [frequency](/source/Frequency) *f*, the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period:[13] f = 1 T = ω 2 π = k 2 π m {\displaystyle f={\frac {1}{T}}={\frac {\omega }{2\pi }}={\frac {\sqrt {k}}{2\pi {\sqrt {m}}}}} ## Theory In [classical physics](/source/Classical_physics), a spring can be seen as a device that stores [potential energy](/source/Potential_energy), specifically [elastic potential energy](/source/Elastic_potential_energy), by straining the bonds between the [atoms](/source/Atom) of an [elastic](/source/Elasticity_(physics)) material. Hooke's law of [elasticity](/source/Theory_of_elasticity) states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its [tension](/source/Tension_(mechanics)), the [force](/source/Force) used to stretch it. Similarly, the contraction (negative extension) is proportional to the [compression](/source/Compression_(physical)) (negative tension). 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 [elastic limit](/source/Tensile_strength), 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. 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 [smooth function](/source/Smooth_function) of one variable approximates a [quadratic function](/source/Quadratic_function) when examined near enough to its minimum point as can be seen by examining the [Taylor series](/source/Taylor_series). Therefore, the force – which is the derivative of energy with respect to displacement – approximates a [linear function](/source/Linear_function). The force of a fully compressed compression coil spring is: F m a x = E d 4 ( L − n d ) 16 ( 1 + ν ) ( D − d ) 3 n {\displaystyle F_{max}={\frac {Ed^{4}(L-nd)}{16(1+\nu )(D-d)^{3}n}}\ } where - E is [Young's modulus](/source/Young's_modulus) - d is the spring wire diameter - L is the free length of the spring - n is the number of active windings - ν is [Poisson's ratio](/source/Poisson's_ratio) - D is the spring outer diameter ## Zero-length springs Simplified LaCoste suspension using a zero-length spring Spring length *L* vs force *F* graph of ordinary (+), zero-length (0) and negative-length (−) springs with the same minimum length *L*0 and spring constant **Zero-length spring** 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. 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 *unwinds* as it stretches), so if it *could* 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 *negative length* spring, made with even more tension so its equilibrium point would be at a *negative* length, with a piece of inelastic material of the proper length so the zero force point would occur at zero length. 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 [period](/source/Period_(physics)). Long-period pendulums enable [seismometers](/source/Seismometer) to sense the slowest waves from earthquakes. The [LaCoste](/source/Lucien_LaCoste) suspension with zero-length springs is also used in [gravimeters](/source/Gravimeter) 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. ## Uses - [Airsoft gun](/source/Airsoft_gun) - [Aerospace](/source/Aerospace) - Retractable [ballpoint pens](/source/Ballpoint_pen) - [Buckling spring](/source/Buckling_spring) keyboards - [Clockwork](/source/Clockwork) clocks, watches, and other things - [Firearms](/source/Firearms) - Forward or aft spring, a method of [mooring](/source/Mooring#Mooring_to_a_shore_fixture) a vessel to a shore fixture - [Gravimeters](/source/Gravimeter) - Industrial Equipment - [Jewelry](/source/Jewelry): Clasp mechanisms - Most [folding knives](/source/Folding_knife), and [switchblades](/source/Switchblade) - [Lock](/source/Lock_(security_device)) mechanisms: Key-recognition and for coordinating the movements of various parts of the lock. - [Spring mattresses](/source/Mattress) - [Medical Devices](/source/Medical_device)[16] - [Pogo Stick](/source/Pogo_Stick) - Pop-open devices: [CD players](/source/CD_player), [tape recorders](/source/Tape_recorder), [toasters](/source/Toaster), etc. - [Spring reverb](/source/Reverb_effect#Spring_reverb) - [Toys](/source/Toy); the [Slinky](/source/Slinky) toy is just a spring - [Trampoline](/source/Trampoline) - [Upholstery coil springs](/source/Upholstery_coil_springs) - [Vehicle suspension](/source/Vehicle_suspension), [Leaf springs](/source/Leaf_springs) ## See also - [Shock absorber](/source/Shock_absorber) - [Slinky](/source/Slinky), helical spring toy ## References 1. **[^](#cite_ref-1)** ["spring"](https://www.oed.com/view/Entry/187725). *[Oxford English Dictionary](/source/Oxford_English_Dictionary)* (online ed.). Oxford University Press. (Subscription or [participating institution membership](https://www.oed.com/public/login/loggingin#withyourlibrary) required.) V. 25. 1. **[^](#cite_ref-2)** [Springs](http://www.madehow.com/Volume-6/Springs.html) How Products Are Made, 14 July 2007. 1. ^ [***a***](#cite_ref-White1966_3-0) [***b***](#cite_ref-White1966_3-1) White, Lynn Jr. (1966). [*Medieval Technology and Social Change*](https://archive.org/details/medievaltechnolo00whit). New York: Oxford Univ. Press. pp. 126–27. [ISBN](/source/ISBN_(identifier)) [0-19-500266-0](https://en.wikipedia.org/wiki/Special:BookSources/0-19-500266-0). 1. **[^](#cite_ref-4)** Usher, Abbot Payson (1988). [*A History of Mechanical Inventions*](https://books.google.com/books?id=xuDDqqa8FlwC&pg=PA305). Courier Dover. p. 305. [ISBN](/source/ISBN_(identifier)) [0-486-25593-X](https://en.wikipedia.org/wiki/Special:BookSources/0-486-25593-X). 1. **[^](#cite_ref-Rossum1997_5-0)** Dohrn-van Rossum, Gerhard (1998). [*History of the Hour: Clocks and Modern Temporal Orders*](https://books.google.com/books?id=53K32RiEigMC&pg=PA121). Univ. of Chicago Press. p. 121. [ISBN](/source/ISBN_(identifier)) [0-226-15510-2](https://en.wikipedia.org/wiki/Special:BookSources/0-226-15510-2). 1. **[^](#cite_ref-6)** Fawcett, W. Peyton (1983), [*History of the Spring Industry*](https://www.americanabookstore.com/pages/books/20947/w-peyton-fawcet/history-of-the-spring-industry-in-the-united-states-and-canada), Spring Manufacturers Institute, Inc., p. 28 1. **[^](#cite_ref-7)** Goetsch, David L. (2005). [*Technical Drawing*](https://books.google.com/books?id=eMqVygLDSa0C&pg=PA577). Cengage Learning. [ISBN](/source/ISBN_(identifier)) [1-4018-5760-4](https://en.wikipedia.org/wiki/Special:BookSources/1-4018-5760-4). 1. **[^](#cite_ref-8)** ["Chevron Spring, - Tedrail"](https://www.tedrail.com/products/classify/Chevron%20Spring). *www.tedrail.com*. Retrieved 23 March 2026. 1. **[^](#cite_ref-9)** Loraine, Jack (17 July 2025). ["Chevron Springs in Railway Suspension Systems | Why Suspension Matters in Modern Railways"](https://www.gmtrubber.com/the-role-of-chevron-springs-in-railway-suspension-systems/). *GMT Rubber*. Retrieved 23 March 2026. 1. **[^](#cite_ref-10)** ["Door Lock Springs"](https://www.springmasters.com/sp/door-lock-springs.html). *www.springmasters.com*. Retrieved 20 March 2018. 1. **[^](#cite_ref-11)** Edwards, Boyd F. (27 October 2017). [*The Ideal Spring and Simple Harmonic Motion*](https://www.youtube.com/watch?v=zoGL52P5VWo) (Video). Utah State University – via YouTube. Based on Cutnell, John D.; Johnson, Kenneth W.; Young, David; Stadler, Shane (2015). "10.1 The Ideal Spring and Simple Harmonic Motion". *Physics*. Hoboken, NJ: Wiley. [ISBN](/source/ISBN_(identifier)) [978-1-118-48689-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-118-48689-4). [OCLC](/source/OCLC_(identifier)) [892304999](https://search.worldcat.org/oclc/892304999). 1. **[^](#cite_ref-12)** Samuel, Andrew; Weir, John (1999). [*Introduction to engineering design: modelling, synthesis and problem solving strategies*](https://archive.org/details/introductiontoen00samu) (2 ed.). Oxford, England: Butterworth. p. [134](https://archive.org/details/introductiontoen00samu/page/n138). [ISBN](/source/ISBN_(identifier)) [0-7506-4282-3](https://en.wikipedia.org/wiki/Special:BookSources/0-7506-4282-3). 1. ^ [***a***](#cite_ref-:02_13-0) [***b***](#cite_ref-:02_13-1) [***c***](#cite_ref-:02_13-2) [***d***](#cite_ref-:02_13-3) [***e***](#cite_ref-:02_13-4) [***f***](#cite_ref-:02_13-5) [***g***](#cite_ref-:02_13-6) ["13.1: The motion of a spring-mass system"](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). *Physics LibreTexts*. 17 September 2019. Retrieved 19 April 2021. 1. **[^](#cite_ref-14)** ["Harmonic motion"](http://labman.phys.utk.edu/phys221core/modules/m11/harmonic_motion.html). *labman.phys.utk.edu*. Retrieved 19 April 2021. 1. **[^](#cite_ref-15)** ["simple harmonic motion | Formula, Examples, & Facts"](https://www.britannica.com/science/simple-harmonic-motion). *Encyclopedia Britannica*. Retrieved 19 April 2021. 1. **[^](#cite_ref-16)** ["Compression Springs"](https://www.coilspringsdirect.com/store/entex-compression-springs). *Coil Springs Direct*. ## Further reading - Sclater, Neil (2011). "Spring and screw devices and mechanisms". *Mechanisms and Mechanical Devices Sourcebook*. 5th ed. New York: McGraw Hill. pp. 279–299. [ISBN](/source/ISBN_(identifier)) [9780071704427](https://en.wikipedia.org/wiki/Special:BookSources/9780071704427). Drawings and designs of various spring and screw mechanisms. - Parmley, Robert (2000). "Section 16: Springs". *Illustrated Sourcebook of Mechanical Components*. New York: McGraw Hill. [ISBN](/source/ISBN_(identifier)) [0070486174](https://en.wikipedia.org/wiki/Special:BookSources/0070486174). Drawings, designs and discussion of various springs and spring mechanisms. - Warden, Tim (2021). "Bundy 2 Alto Saxophone". This saxophone is known for having the strongest tensioned needle springs in existence. ## External links Wikimedia Commons has media related to [Spring (device)](https://commons.wikimedia.org/wiki/Spring_(device)). - Paredes, Manuel (2013). ["How to design springs"](http://www.meca.insa-toulouse.fr/~paredes/Springs2K/index.php). insa de toulouse. Retrieved 13 November 2013. - Silberstein, Dave (2002). ["How to make springs"](https://web.archive.org/web/20130918155928/http://home.earthlink.net/~bazillion/intro.html). Bazillion. Archived from [the original](https://home.earthlink.net/~bazillion/intro.html) on 18 September 2013. Retrieved 3 February 2008. - Wright, Douglas. ["Introduction to Springs"](http://www.mech.uwa.edu.au/DANotes/springs/intro/intro.html). *Notes on Design and Analysis of Machine Elements*. Department of Mechanical & Material Engineering, [University of Western Australia](/source/University_of_Western_Australia). Retrieved 3 February 2008. - [Springs with Dynamically Variable Stiffness (patent)](https://patents.google.com/patent/WO2017077541A9/en) - [Smart Springs and their Combinations (patent)](https://patents.google.com/patent/US20170051808A1/en) v t e Machines Classical simple machines Inclined plane Lever Pulley Screw Wedge Wheel and axle Clocks Atomic clock Chronometer Pendulum clock Quartz clock Compressors and pumps Archimedes' screw Eductor-jet pump Hydraulic ram Pump Trompe Vacuum pump External combustion engines Steam engine Stirling engine Internal combustion engines Gas turbine Reciprocating engine Rotary engine Nutating disc engine Linkages Pantograph Peaucellier-Lipkin Turbine Gas turbine Jet engine Steam turbine Water turbine Wind generator Windmill Aerofoil Sail Wing Rudder Flap Propeller Electronics Vacuum tube Transistor Diode Resistor Capacitor Inductor Vehicles Automobile Miscellaneous Mecha Robot Agricultural Seed-counting machine Vending machine Wind tunnel Check weighing machines Riveting machines Springs Spring (device) Authority control databases International GND FAST National United States France BnF data Japan Czech Republic Israel Other Yale LUX --- Adapted from the Wikipedia article [Spring (device)](https://en.wikipedia.org/wiki/Spring_(device)) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Spring_(device)?action=history)). 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