309:
2088:
340:
519:
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.
2096:
293:
96:
52:
80:
88:
945:
317:
60:
38:
352:
368:
1885:, 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.
360:
2121:
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.
2133:
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,
859:
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
283:
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
518:
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.
451:
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,
2145:
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
329:
2704:
1263:
1830:
2029:
1738:
2162:
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
686:
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
1142:
647:
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.
939:
1577:
1496:
1419:
837:
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
1035:
2125:
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
430:
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
1671:
209:/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
762:
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:
506:
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.
1161:
1881:
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
697:
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.
848:
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
216:
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
269:
appeared early in the 15th century, in door locks. The first spring powered-clocks appeared in that century and evolved into the first large watches by the 16th century.
1754:
801:
126:
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. Springs can
2475:
1613:
2070:
1331:
1305:
1285:
1062:
856:
2122:"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.
157:
When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing
83:
Force (F) vs extension (s). Spring characteristics: (1) progressive, (2) linear, (3) degressive, (4) almost constant, (5) progressive with knee
512:
are designed to become shorter when loaded. Their turns (loops) are not touching in the unloaded position, and they need no attachment points.
263:
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.
1913:
1888:
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
1684:
1307:
are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with
960:
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
2831:
Warden, Tim. (2021). “Bundy 2 Alto
Saxophone.” This saxophone is known for having the strongest tensioned needle springs in existence.
1070:
1749:, the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period:
2596:
Cutnell, John D.; Johnson, Kenneth W.; Young, David; Stadler, Shane (2015). "10.1 The Ideal Spring and Simple
Harmonic Motion".
2884:
2605:
233:
1866:
states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its
888:
621:
A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated
1528:
1447:
1370:
2937:
970:
2810:
2673:
2646:
2458:
2431:
2404:
2142:
length, with a piece of inelastic material of the proper length so the zero force point would occur at zero length.
1641:
2868:
1679:, the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by:
676:
284:
United States in 1847, John Evans' Sons became "America's oldest springmaker" which continues to operate today.
161:
approximately proportional to its change in length (this approximation breaks down for larger deflections). The
3319:
3146:
2825:
3381:
1258:{\displaystyle x(t)=A\sin \left(t{\sqrt {\frac {k}{m}}}\right)+B\cos \left(t{\sqrt {\frac {k}{m}}}\right).\,}
2730:
1626:ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant
1900:. Therefore, the force – which is the derivative of energy with respect to displacement – approximates a
529:
A pre-curved or arc-shaped helical compression spring, which is able to transmit a torque around an axis.
17:
3100:
3077:
408:
Unlike the above types in which the load is an axial force, the load applied to a torsion spring is a
255:(and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of
2982:
2348:
541:
so that under compression the coils are not forced against each other, thus permitting longer travel.
400:
Designed to operate with a compression load, so the spring gets shorter as the load is applied to it.
2780:
2544:
2107:
graph of ordinary (+), zero-length (0) and negative-length (−) springs with the same minimum length
1333:(zero initial position with some positive initial velocity) is displayed in the image on the right.
819:
is the resulting force vector – the magnitude and direction of the restoring force the spring exerts
494:
Also known as a helical spring. A spring (made by winding a wire around a cylinder) is of two types:
1848:
197:
proportional to the angle. A torsion spring's rate is in units of torque divided by angle, such as
170:
1825:{\displaystyle f={\frac {1}{T}}={\frac {\omega }{2\pi }}={\frac {1}{2\pi }}{\sqrt {\frac {k}{m}}}}
189:
spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in. A
2353:
2288:
727:
260:
193:
is a spring that works by twisting; when it is twisted about its axis by an angle, it produces a
31:
2843:
2977:
2930:
2638:
2232:
1875:
1508:
1342:
841:
Most real springs approximately follow Hooke's law if not stretched or compressed beyond their
217:
186:
2860:
2663:
2448:
2421:
768:
308:
134:, but there are many different spring designs. Modern springs are typically manufactured from
3324:
2531:
2361:
1041:
681:
628:
412:
or twisting force, and the end of the spring rotates through an angle as the load is applied.
2755:
2630:
2235:
mechanisms: Key-recognition and for coordinating the movements of various parts of the lock.
2207:
3232:
3133:
3123:
3113:
3042:
2268:
2087:
1874:
used to stretch it. Similarly, the contraction (negative extension) is proportional to the
1863:
1856:
1586:
570:
123:
2558:
2502:
2490:
2055:
8:
1867:
1310:
869:
709:
3010:
2908:
2633:
Introduction to engineering design: modelling, synthesis and problem solving strategies
2293:
2039:
1893:
1290:
1270:
1047:
691:
any tendency to re-wind. The most common application is the retracting steel tape rule.
2903:
2515:
3344:
2923:
2821:
2806:
2669:
2642:
2631:
2611:
2601:
2454:
2427:
2400:
2393:
1840:
1623:
1581:
Since there is no energy loss in such a system, energy is always conserved and thus:
616:
557:, and places where electricity must be carried to partially rotating devices such as
391:
221:
182:
1427:
of the wave-like motion that is produced by the oscillating behavior of the spring.
952:, as a function of time. The amount of time that passes between peaks is called the
339:
2888:
2147:
1882:
1844:
1350:
240:
236:
71:, measuring 2 m (6 ft 7 in) long, with a 470 N (105 lbf)
3329:
3227:
3090:
2189:
1901:
1889:
538:
225:
64:
324:. Under compression the coils slide over each other, so affording longer travel.
280:, which states that the force a spring exerts is proportional to its extension.
3189:
3030:
3015:
2987:
2962:
2954:
2375:
2310:
2243:
2155:
1896:
when examined near enough to its minimum point as can be seen by examining the
1501:
1354:
1346:
757:
721:
600:
558:
544:
466:
A coiled steel spring that is connected at each end to create a circular shape.
403:
277:
266:
190:
127:
2584:
726:
Any spring designed to be twisted rather than compressed or extended. Used in
383:
Springs can be classified depending on how the load force is applied to them:
3375:
3339:
3184:
3179:
3118:
3052:
2615:
2321:
2258:
2223:
2184:
2073:
1897:
842:
633:
A tightly rolled ribbon that exerts a nearly constant force as it is unrolled
532:
461:
321:
143:
736:
various types of spring made compact by using waves to give a spring effect.
292:
251:
Simple non-coiled springs have been used throughout human history, e.g. the
3174:
3085:
3020:
3005:
2297:
2138:
spring, made with even more tension so its equilibrium point would be at a
2095:
1353:, but the total energy of the system remains the same. A spring that obeys
578:
554:
442:
347:
and arc spring systems (systems consisting of inner and outer arc springs).
273:
252:
210:
198:
169:
of a spring is the change in the force it exerts, divided by the change in
139:
135:
91:
A machined spring incorporates several features into one piece of bar stock
68:
2828:
Drawings, designs and discussion of various springs and spring mechanisms.
95:
3334:
3250:
3242:
3164:
3108:
3067:
2227:
2173:
2151:
953:
741:
700:
564:
489:
371:
333:
301:
131:
72:
51:
44:
2342:
359:
3293:
3255:
3169:
3141:
2283:
2248:
2159:
961:
650:
636:
603:
locks. Also door-lock spring, as used in antique door latch mechanisms.
524:
483:
344:
297:
112:
100:
2516:"Springs with dynamically variable stiffness and actuation capability"
2024:{\displaystyle F_{max}={\frac {Ed^{4}(L-nd)}{16(1+\nu )(D-d)^{3}n}}\ }
1733:{\displaystyle T={\frac {2\pi }{\omega }}=2\pi {\sqrt {\frac {m}{k}}}}
3270:
2254:
2195:
2178:
1743:
1424:
849:
668:
656:
622:
596:
592:
206:
3275:
3265:
3194:
3047:
2238:
2201:
1516:
715:
705:
A tension spring where energy is stored by stretching the material.
458:
A zig-zag of thick wire, often used in modern upholstery/furniture.
256:
229:
174:
147:
108:
2801:
Sclater, Neil. (2011). "Spring and screw devices and mechanisms."
882:, the force equation for a spring obeying Hooke's law looks like:
87:
3285:
3204:
3156:
2946:
2262:
2216:
588:
316:
79:
59:
944:
130:
when compressed. In everyday use, the term most often refers to
3222:
3062:
2972:
2315:
2277:
1434:
of such a system can be determined through the spring constant
1152:
574:
409:
328:
202:
194:
2813:. Drawings and designs of various spring and screw mechanisms.
37:
3314:
3309:
3260:
2997:
2967:
1871:
1137:{\displaystyle {\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0,\,}
664:
660:
550:
549:
Also known as a hairspring. A delicate spiral spring used in
178:
158:
151:
55:
A heavy-duty coil spring designed for compression and tension
41:
3217:
3212:
3057:
3034:
2915:
1852:
1148:
714:
Used to apply a constant tensile force along the axis of a
418:
Supported load remains the same throughout deflection cycle
394:
load, so the spring stretches as the load is applied to it.
351:
104:
2595:
2756:"simple harmonic motion | Formula, Examples, & Facts"
2273:
672:
367:
2091:
Simplified LaCoste suspension using a zero-length spring
424:
Resistance of the coil to load varies during compression
2867:. Department of Mechanical & Material Engineering,
1345:
of a spring-mass system, energy will fluctuate between
655:
A spiral ribbon-shaped spring used as a power store of
2505:
Piping
Technology and Products, (retrieved March 2012)
2493:
Piping
Technology and Products, (retrieved March 2012)
2450:
History of the Hour: Clocks and Modern
Temporal Orders
355:
Tension springs in a folded line reverberation device.
2058:
1916:
1757:
1687:
1644:
1589:
1531:
1450:
1373:
1313:
1293:
1273:
1164:
1073:
1050:
973:
934:{\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,}
891:
771:
2904:
2637:(2 ed.). Oxford, England: Butterworth. p.
2158:
suspension with zero-length springs is also used in
1572:{\displaystyle K=\left({\frac {1}{2}}\right)mv^{2}}
1511:can be found using the mass of the attached object
1491:{\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}}
1414:{\displaystyle E=\left({\frac {1}{2}}\right)kA^{2}}
2480:, Spring Manufacturers Institute, Inc., p. 28
2392:
2341:
2064:
2023:
1824:
1732:
1665:
1607:
1571:
1490:
1413:
1325:
1299:
1279:
1257:
1136:
1056:
1029:
933:
795:
434:They can also be classified based on their shape:
232:for parts requiring corrosion resistance, and low-
75:, with each limb functionally a cantilever spring.
2805:5th ed. New York: McGraw Hill. pp. 279–299.
2399:. New York: Oxford Univ. Press. pp. 126–27.
2154:to sense the slowest waves from earthquakes. The
3373:
2865:Notes on Design and Analysis of Machine Elements
2818:Illustrated Sourcebook of Mechanical Components.
2816:Parmley, Robert. (2000). "Section 16: Springs."
2628:
2446:
2340:
1030:{\displaystyle -kx=m{\frac {d^{2}x}{dt^{2}}}.\,}
813:is the displacement vector – the distance and h.
1843:, a spring can be seen as a device that stores
1666:{\displaystyle \omega ={\sqrt {\frac {k}{m}}}}
855:If made with constant pitch (wire thickness),
2931:
2909:Smart Springs and their Combinations (patent)
2803:Mechanisms and Mechanical Devices Sourcebook.
312:Battery contacts often have a variable spring
213:, as is the compliance of springs in series.
138:. An example of a non-metallic spring is the
2592:. Utah State University – via YouTube.
486:, while the free-hanging end takes the load.
67:– a simple but very powerful spring made of
27:Elastic object that stores mechanical energy
2882:
2586:The Ideal Spring and Simple Harmonic Motion
2386:
2384:
537:A compression coil spring in the form of a
482:A flat spring fixed only at one end like a
220:steel and hardened after manufacture. Some
2938:
2924:
2705:"13.1: The motion of a spring-mass system"
2440:
1617:
1254:
1133:
1026:
930:
863:
390:The spring is designed to operate with a
2381:
2094:
2086:
943:
366:
358:
350:
338:
327:
315:
307:
291:
94:
86:
78:
58:
50:
36:
2841:
2661:
2582:
2473:
2453:. Univ. of Chicago Press. p. 121.
1630:and the mass of the oscillating object
14:
3374:
2699:
2697:
2695:
2693:
2691:
2689:
2687:
2685:
2082:
1147:the solution of which is the sum of a
2919:
2419:
2395:Medieval Technology and Social Change
2390:
1851:, by straining the bonds between the
475:The most common types of spring are:
2583:Edwards, Boyd F. (27 October 2017).
2378:How Products Are Made, 14 July 2007.
2362:participating institution membership
1064:as a function of time. Rearranging:
2682:
2629:Samuel, Andrew; Weir, John (1999).
2206:Forward or aft spring, a method of
24:
2858:
2795:
2447:Dohrn-van Rossum, Gerhard (1998).
2423:A History of Mechanical Inventions
1336:
173:of the spring. That is, it is the
142:, made traditionally of flexible
25:
3393:
2835:
2198:clocks, watches, and other things
1907:Force of fully compressed spring
378:
2134:so they are made by combining a
1361:will have a total system energy
677:mechanically powered flashlights
363:A torsion bar twisted under load
2869:University of Western Australia
2773:
2748:
2723:
2655:
2622:
2576:
2551:
2150:. Long-period pendulums enable
1892:of one variable approximates a
1519:at which the object oscillates
908:
904:
561:without hindering the rotation.
470:
177:of the force versus deflection
2508:
2496:
2484:
2477:History of the Spring Industry
2467:
2426:. Courier Dover. p. 305.
2413:
2369:
2334:
2003:
1990:
1987:
1975:
1967:
1952:
1174:
1168:
1040:This is a second order linear
905:
874:Since force is equal to mass,
751:
607:
569:A flat spring used in vehicle
13:
1:
2327:
2050:n – number of active windings
694:Progressive rate coil springs
122:is a device consisting of an
2945:
2420:Usher, Abbot Payson (1988).
296:A spiral torsion spring, or
7:
3101:Internal combustion engines
3078:External combustion engines
2887:. Bazillion. Archived from
2474:Fawcett, W. Peyton (1983),
2304:
2210:a vessel to a shore fixture
2129:as it stretches), so if it
964:of x with respect to time,
730:vehicle suspension systems.
641:A volume of compressed gas.
332:Vertical volute springs of
150:stores energy to propel an
10:
3398:
2883:Silberstein, Dave (2002).
2662:Goetsch, David L. (2005).
867:
755:
746:
739:
272:In 1676 British physicist
246:
29:
3353:
3302:
3284:
3241:
3203:
3155:
3132:
3099:
3076:
3029:
2996:
2955:Classical simple machines
2953:
2861:"Introduction to Springs"
2349:Oxford English Dictionary
2078:D – spring outer diameter
2047:L – free length of spring
1834:
427:Variable stiffness spring
224:are also used, including
107:(normally connected to a
2842:Paredes, Manuel (2013).
2503:Variable Spring Supports
2391:White, Lynn Jr. (1966).
2044:d – spring wire diameter
1849:elastic potential energy
796:{\displaystyle F=-kx,\ }
387:Tension/extension spring
287:
111:) showing spring-loaded
3340:Check weighing machines
2844:"How to design springs"
2820:New York: McGraw Hill.
2760:Encyclopedia Britannica
2526:– via google.com.
2354:Oxford University Press
2289:Upholstery coil springs
2166:
591:mechanisms such as the
261:Ctesibius of Alexandria
32:Spring (disambiguation)
2600:. Hoboken, NJ: Wiley.
2539:Cite journal requires
2115:
2092:
2066:
2025:
1826:
1734:
1667:
1618:Frequency & period
1609:
1573:
1509:simple harmonic motion
1492:
1415:
1343:simple harmonic motion
1327:
1301:
1281:
1259:
1138:
1058:
1031:
957:
935:
878:, times acceleration,
864:Simple harmonic motion
797:
375:
364:
356:
348:
336:
325:
313:
305:
115:
92:
84:
76:
56:
48:
3325:Seed-counting machine
2885:"How to make springs"
2781:"Compression Springs"
2563:www.springmasters.com
2098:
2090:
2067:
2026:
1827:
1735:
1668:
1610:
1608:{\displaystyle E=K+U}
1574:
1493:
1438:and its displacement
1430:The potential energy
1416:
1357:with spring constant
1328:
1302:
1282:
1260:
1139:
1059:
1044:for the displacement
1042:differential equation
1032:
947:
936:
798:
629:Constant-force spring
612:Other types include:
516:Hollow tubing springs
370:
362:
354:
343:Selection of various
342:
331:
319:
311:
295:
239:for springs carrying
98:
90:
82:
62:
54:
40:
3382:Springs (mechanical)
3124:Nutating disc engine
3114:Reciprocating engine
2891:on 18 September 2013
2668:. Cengage Learning.
2318:, helical spring toy
2280:toy is just a spring
2213:Industrial Equipment
2065:{\displaystyle \nu }
2056:
1914:
1878:(negative tension).
1755:
1685:
1642:
1587:
1529:
1448:
1371:
1311:
1291:
1271:
1162:
1071:
1048:
971:
889:
769:
47:designed for tension
30:For other uses, see
2785:Coil Springs Direct
2735:labman.phys.utk.edu
2711:. 17 September 2019
2559:"Door Lock Springs"
2352:(Online ed.).
2114:and spring constant
2083:Zero-length springs
1326:{\displaystyle B=0}
870:Harmonic oscillator
852:with displacement.
510:Compression springs
103:firing device from
3147:Peaucellier-Lipkin
2846:. insa de toulouse
2709:Physics LibreTexts
2294:Vehicle suspension
2253:Pop-open devices:
2219:: Clasp mechanisms
2119:Zero-length spring
2116:
2093:
2062:
2021:
1894:quadratic function
1822:
1730:
1663:
1605:
1569:
1488:
1411:
1323:
1297:
1277:
1255:
1134:
1054:
1027:
958:
948:The displacement,
931:
793:
397:Compression spring
376:
365:
357:
349:
337:
326:
314:
306:
259:in many cultures.
222:non-ferrous metals
116:
93:
85:
77:
57:
49:
3369:
3368:
3345:Riveting machines
3043:Archimedes' screw
2859:Wright, Douglas.
2731:"Harmonic motion"
2665:Technical Drawing
2607:978-1-118-48689-4
2518:. 3 November 2016
2360:(Subscription or
2239:Spring mattresses
2020:
2016:
1841:classical physics
1820:
1819:
1808:
1790:
1772:
1728:
1727:
1707:
1661:
1660:
1624:angular frequency
1550:
1469:
1392:
1300:{\displaystyle B}
1280:{\displaystyle A}
1244:
1243:
1207:
1206:
1119:
1106:
1057:{\displaystyle x}
1021:
792:
617:Belleville washer
504:extension springs
479:Cantilever spring
455:Serpentine spring
146:wood, which when
16:(Redirected from
3389:
3048:Eductor-jet pump
2940:
2933:
2926:
2917:
2916:
2900:
2898:
2896:
2879:
2877:
2875:
2855:
2853:
2851:
2789:
2788:
2777:
2771:
2770:
2768:
2766:
2752:
2746:
2745:
2743:
2741:
2727:
2721:
2720:
2718:
2716:
2701:
2680:
2679:
2659:
2653:
2652:
2636:
2626:
2620:
2619:
2593:
2591:
2580:
2574:
2573:
2571:
2569:
2555:
2549:
2548:
2542:
2537:
2535:
2527:
2525:
2523:
2512:
2506:
2500:
2494:
2491:Constant Springs
2488:
2482:
2481:
2471:
2465:
2464:
2444:
2438:
2437:
2417:
2411:
2410:
2398:
2388:
2379:
2373:
2367:
2365:
2357:
2345:
2338:
2071:
2069:
2068:
2063:
2030:
2028:
2027:
2022:
2018:
2017:
2015:
2011:
2010:
1970:
1951:
1950:
1937:
1932:
1931:
1845:potential energy
1831:
1829:
1828:
1823:
1821:
1812:
1811:
1809:
1807:
1796:
1791:
1789:
1778:
1773:
1765:
1739:
1737:
1736:
1731:
1729:
1720:
1719:
1708:
1703:
1695:
1672:
1670:
1669:
1664:
1662:
1653:
1652:
1614:
1612:
1611:
1606:
1578:
1576:
1575:
1570:
1568:
1567:
1555:
1551:
1543:
1507:of an object in
1497:
1495:
1494:
1489:
1487:
1486:
1474:
1470:
1462:
1420:
1418:
1417:
1412:
1410:
1409:
1397:
1393:
1385:
1351:potential energy
1332:
1330:
1329:
1324:
1306:
1304:
1303:
1298:
1286:
1284:
1283:
1278:
1264:
1262:
1261:
1256:
1250:
1246:
1245:
1236:
1235:
1213:
1209:
1208:
1199:
1198:
1143:
1141:
1140:
1135:
1120:
1112:
1107:
1105:
1104:
1103:
1090:
1086:
1085:
1075:
1063:
1061:
1060:
1055:
1036:
1034:
1033:
1028:
1022:
1020:
1019:
1018:
1005:
1001:
1000:
990:
940:
938:
937:
932:
802:
800:
799:
794:
790:
587:Used in antique
241:electric current
237:beryllium copper
21:
3397:
3396:
3392:
3391:
3390:
3388:
3387:
3386:
3372:
3371:
3370:
3365:
3361:Spring (device)
3349:
3330:Vending machine
3298:
3280:
3237:
3199:
3151:
3128:
3095:
3091:Stirling engine
3072:
3025:
2992:
2949:
2944:
2894:
2892:
2873:
2871:
2849:
2847:
2838:
2798:
2796:Further reading
2793:
2792:
2779:
2778:
2774:
2764:
2762:
2754:
2753:
2749:
2739:
2737:
2729:
2728:
2724:
2714:
2712:
2703:
2702:
2683:
2676:
2660:
2656:
2649:
2627:
2623:
2608:
2589:
2581:
2577:
2567:
2565:
2557:
2556:
2552:
2540:
2538:
2529:
2528:
2521:
2519:
2514:
2513:
2509:
2501:
2497:
2489:
2485:
2472:
2468:
2461:
2445:
2441:
2434:
2418:
2414:
2407:
2389:
2382:
2374:
2370:
2359:
2339:
2335:
2330:
2307:
2302:
2244:Medical Devices
2190:Buckling spring
2169:
2136:negative length
2113:
2085:
2057:
2054:
2053:
2040:Young's modulus
2006:
2002:
1971:
1946:
1942:
1938:
1936:
1921:
1917:
1915:
1912:
1911:
1902:linear function
1890:smooth function
1862:Hooke's law of
1847:, specifically
1837:
1810:
1800:
1795:
1782:
1777:
1764:
1756:
1753:
1752:
1718:
1696:
1694:
1686:
1683:
1682:
1651:
1643:
1640:
1639:
1620:
1588:
1585:
1584:
1563:
1559:
1542:
1538:
1530:
1527:
1526:
1482:
1478:
1461:
1457:
1449:
1446:
1445:
1423:Here, A is the
1405:
1401:
1384:
1380:
1372:
1369:
1368:
1339:
1337:Energy dynamics
1312:
1309:
1308:
1292:
1289:
1288:
1272:
1269:
1268:
1234:
1230:
1226:
1197:
1193:
1189:
1163:
1160:
1159:
1111:
1099:
1095:
1091:
1081:
1077:
1076:
1074:
1072:
1069:
1068:
1049:
1046:
1045:
1014:
1010:
1006:
996:
992:
991:
989:
972:
969:
968:
890:
887:
886:
872:
866:
857:conical springs
831:spring constant
770:
767:
766:
760:
754:
749:
744:
610:
559:steering wheels
473:
448:Machined spring
441:Made of a flat
421:Variable spring
415:Constant spring
381:
290:
249:
226:phosphor bronze
167:spring constant
65:English longbow
35:
28:
23:
22:
15:
12:
11:
5:
3395:
3385:
3384:
3367:
3366:
3364:
3363:
3357:
3355:
3351:
3350:
3348:
3347:
3342:
3337:
3332:
3327:
3322:
3317:
3312:
3306:
3304:
3300:
3299:
3297:
3296:
3290:
3288:
3282:
3281:
3279:
3278:
3273:
3268:
3263:
3258:
3253:
3247:
3245:
3239:
3238:
3236:
3235:
3230:
3225:
3220:
3215:
3209:
3207:
3201:
3200:
3198:
3197:
3192:
3190:Wind generator
3187:
3182:
3177:
3172:
3167:
3161:
3159:
3153:
3152:
3150:
3149:
3144:
3138:
3136:
3130:
3129:
3127:
3126:
3121:
3116:
3111:
3105:
3103:
3097:
3096:
3094:
3093:
3088:
3082:
3080:
3074:
3073:
3071:
3070:
3065:
3060:
3055:
3050:
3045:
3039:
3037:
3027:
3026:
3024:
3023:
3018:
3016:Pendulum clock
3013:
3008:
3002:
3000:
2994:
2993:
2991:
2990:
2988:Wheel and axle
2985:
2980:
2975:
2970:
2965:
2963:Inclined plane
2959:
2957:
2951:
2950:
2943:
2942:
2935:
2928:
2920:
2912:
2911:
2906:
2901:
2880:
2856:
2837:
2836:External links
2834:
2833:
2832:
2829:
2814:
2797:
2794:
2791:
2790:
2772:
2747:
2722:
2681:
2674:
2654:
2647:
2621:
2606:
2575:
2550:
2541:|journal=
2507:
2495:
2483:
2466:
2459:
2439:
2432:
2412:
2405:
2380:
2368:
2332:
2331:
2329:
2326:
2325:
2324:
2319:
2313:
2311:Shock absorber
2306:
2303:
2301:
2300:
2291:
2286:
2281:
2271:
2266:
2259:tape recorders
2251:
2246:
2241:
2236:
2230:
2224:folding knives
2220:
2214:
2211:
2204:
2199:
2193:
2187:
2185:ballpoint pens
2181:
2176:
2170:
2168:
2165:
2111:
2099:Spring length
2084:
2081:
2080:
2079:
2076:
2061:
2051:
2048:
2045:
2042:
2032:
2031:
2014:
2009:
2005:
2001:
1998:
1995:
1992:
1989:
1986:
1983:
1980:
1977:
1974:
1969:
1966:
1963:
1960:
1957:
1954:
1949:
1945:
1941:
1935:
1930:
1927:
1924:
1920:
1836:
1833:
1818:
1815:
1806:
1803:
1799:
1794:
1788:
1785:
1781:
1776:
1771:
1768:
1763:
1760:
1726:
1723:
1717:
1714:
1711:
1706:
1702:
1699:
1693:
1690:
1659:
1656:
1650:
1647:
1619:
1616:
1604:
1601:
1598:
1595:
1592:
1566:
1562:
1558:
1554:
1549:
1546:
1541:
1537:
1534:
1502:kinetic energy
1485:
1481:
1477:
1473:
1468:
1465:
1460:
1456:
1453:
1408:
1404:
1400:
1396:
1391:
1388:
1383:
1379:
1376:
1347:kinetic energy
1338:
1335:
1322:
1319:
1316:
1296:
1276:
1266:
1265:
1253:
1249:
1242:
1239:
1233:
1229:
1225:
1222:
1219:
1216:
1212:
1205:
1202:
1196:
1192:
1188:
1185:
1182:
1179:
1176:
1173:
1170:
1167:
1145:
1144:
1132:
1129:
1126:
1123:
1118:
1115:
1110:
1102:
1098:
1094:
1089:
1084:
1080:
1053:
1038:
1037:
1025:
1017:
1013:
1009:
1004:
999:
995:
988:
985:
982:
979:
976:
942:
941:
929:
926:
923:
920:
917:
914:
911:
907:
903:
900:
897:
894:
868:Main article:
865:
862:
839:
838:
835:force constant
820:
814:
804:
803:
789:
786:
783:
780:
777:
774:
756:Main article:
753:
750:
748:
745:
740:Main article:
738:
737:
734:
731:
724:
722:Torsion spring
719:
712:
706:
703:
698:
695:
692:
684:
682:Negator spring
679:
653:
648:
645:
642:
639:
634:
631:
626:
619:
609:
606:
605:
604:
601:percussion cap
585:
582:
567:
562:
547:
545:Balance spring
542:
535:
530:
527:
521:
520:
513:
507:
496:
495:
492:
487:
480:
472:
469:
468:
467:
464:
459:
456:
453:
449:
446:
439:
432:
431:
428:
425:
422:
419:
416:
413:
406:
404:Torsion spring
401:
398:
395:
388:
380:
379:Classification
377:
289:
286:
267:Coiled springs
248:
245:
191:torsion spring
26:
9:
6:
4:
3:
2:
3394:
3383:
3380:
3379:
3377:
3362:
3359:
3358:
3356:
3352:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3307:
3305:
3303:Miscellaneous
3301:
3295:
3292:
3291:
3289:
3287:
3283:
3277:
3274:
3272:
3269:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3248:
3246:
3244:
3240:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3210:
3208:
3206:
3202:
3196:
3193:
3191:
3188:
3186:
3185:Water turbine
3183:
3181:
3180:Steam turbine
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3162:
3160:
3158:
3154:
3148:
3145:
3143:
3140:
3139:
3137:
3135:
3131:
3125:
3122:
3120:
3119:Rotary engine
3117:
3115:
3112:
3110:
3107:
3106:
3104:
3102:
3098:
3092:
3089:
3087:
3084:
3083:
3081:
3079:
3075:
3069:
3066:
3064:
3061:
3059:
3056:
3054:
3053:Hydraulic ram
3051:
3049:
3046:
3044:
3041:
3040:
3038:
3036:
3032:
3028:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3003:
3001:
2999:
2995:
2989:
2986:
2984:
2981:
2979:
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2960:
2958:
2956:
2952:
2948:
2941:
2936:
2934:
2929:
2927:
2922:
2921:
2918:
2914:
2910:
2907:
2905:
2902:
2890:
2886:
2881:
2870:
2866:
2862:
2857:
2845:
2840:
2839:
2830:
2827:
2823:
2819:
2815:
2812:
2811:9780071704427
2808:
2804:
2800:
2799:
2786:
2782:
2776:
2761:
2757:
2751:
2736:
2732:
2726:
2710:
2706:
2700:
2698:
2696:
2694:
2692:
2690:
2688:
2686:
2677:
2675:1-4018-5760-4
2671:
2667:
2666:
2658:
2650:
2648:0-7506-4282-3
2644:
2640:
2635:
2634:
2625:
2617:
2613:
2609:
2603:
2599:
2588:
2587:
2579:
2564:
2560:
2554:
2546:
2533:
2517:
2511:
2504:
2499:
2492:
2487:
2479:
2478:
2470:
2462:
2460:0-226-15510-2
2456:
2452:
2451:
2443:
2435:
2433:0-486-25593-X
2429:
2425:
2424:
2416:
2408:
2406:0-19-500266-0
2402:
2397:
2396:
2387:
2385:
2377:
2372:
2363:
2355:
2351:
2350:
2344:
2337:
2333:
2323:
2322:Volute spring
2320:
2317:
2314:
2312:
2309:
2308:
2299:
2295:
2292:
2290:
2287:
2285:
2282:
2279:
2275:
2272:
2270:
2269:Spring reverb
2267:
2264:
2260:
2256:
2252:
2250:
2247:
2245:
2242:
2240:
2237:
2234:
2231:
2229:
2225:
2221:
2218:
2215:
2212:
2209:
2205:
2203:
2200:
2197:
2194:
2191:
2188:
2186:
2182:
2180:
2177:
2175:
2172:
2171:
2164:
2161:
2157:
2153:
2149:
2143:
2141:
2137:
2132:
2128:
2123:
2120:
2110:
2106:
2102:
2097:
2089:
2077:
2075:
2074:Poisson ratio
2059:
2052:
2049:
2046:
2043:
2041:
2037:
2036:
2035:
2012:
2007:
1999:
1996:
1993:
1984:
1981:
1978:
1972:
1964:
1961:
1958:
1955:
1947:
1943:
1939:
1933:
1928:
1925:
1922:
1918:
1910:
1909:
1908:
1905:
1903:
1899:
1898:Taylor series
1895:
1891:
1886:
1884:
1883:elastic limit
1879:
1877:
1873:
1869:
1865:
1860:
1858:
1854:
1850:
1846:
1842:
1832:
1816:
1813:
1804:
1801:
1797:
1792:
1786:
1783:
1779:
1774:
1769:
1766:
1761:
1758:
1750:
1748:
1745:
1740:
1724:
1721:
1715:
1712:
1709:
1704:
1700:
1697:
1691:
1688:
1680:
1678:
1673:
1657:
1654:
1648:
1645:
1637:
1636:
1633:
1629:
1625:
1615:
1602:
1599:
1596:
1593:
1590:
1582:
1579:
1564:
1560:
1556:
1552:
1547:
1544:
1539:
1535:
1532:
1524:
1522:
1518:
1514:
1510:
1506:
1503:
1498:
1483:
1479:
1475:
1471:
1466:
1463:
1458:
1454:
1451:
1443:
1441:
1437:
1433:
1428:
1426:
1421:
1406:
1402:
1398:
1394:
1389:
1386:
1381:
1377:
1374:
1366:
1364:
1360:
1356:
1352:
1348:
1344:
1334:
1320:
1317:
1314:
1294:
1274:
1251:
1247:
1240:
1237:
1231:
1227:
1223:
1220:
1217:
1214:
1210:
1203:
1200:
1194:
1190:
1186:
1183:
1180:
1177:
1171:
1165:
1158:
1157:
1156:
1154:
1150:
1130:
1127:
1124:
1121:
1116:
1113:
1108:
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3320:Agricultural
3175:Quasiturbine
3086:Steam engine
3021:Quartz clock
3006:Atomic clock
2913:
2893:. Retrieved
2889:the original
2872:. Retrieved
2864:
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2817:
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2759:
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2562:
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2422:
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2394:
2371:
2347:
2336:
2298:Leaf springs
2228:switchblades
2183:Retractable
2152:seismometers
2144:
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816:
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761:
688:
659:mechanisms:
644:Ideal spring
611:
515:
509:
503:
499:
474:
471:Common types
443:spring steel
433:
382:
282:
274:Robert Hooke
271:
265:
250:
215:
166:
162:
156:
136:spring steel
132:coil springs
128:store energy
119:
117:
45:coil springs
3335:Wind tunnel
3251:Vacuum tube
3243:Electronics
3165:Gas turbine
3109:Gas turbine
3068:Vacuum pump
3031:Compressors
3011:Chronometer
2850:13 November
2174:Airsoft gun
2160:gravimeters
1876:compression
1675:The period
1355:Hooke's Law
850:nonlinearly
758:Hooke's law
752:Hooke's law
742:Wave spring
733:Wave spring
728:torsion bar
701:Rubber band
669:music boxes
608:Other types
571:suspensions
565:Leaf spring
490:Coil spring
438:Flat spring
372:Leaf spring
345:arc springs
334:Stuart tank
302:alarm clock
278:Hooke's law
276:postulated
187:compression
73:draw weight
18:Spring rate
3294:Automobile
3256:Transistor
3170:Jet engine
3142:Pantograph
2895:3 February
2874:3 February
2826:0070486174
2364:required.)
2328:References
2284:Trampoline
2255:CD players
2249:Pogo Stick
1864:elasticity
1859:material.
962:derivative
860:deformed.
651:Mainspring
637:Gas spring
525:Arc spring
484:cantilever
374:on a truck
298:hairspring
234:resistance
171:deflection
113:firing pin
101:booby trap
3271:Capacitor
3233:Propeller
2616:892304999
2594:Based on
2196:Clockwork
2192:keyboards
2179:Aerospace
2103:vs force
2060:ν
1997:−
1985:ν
1959:−
1805:π
1787:π
1780:ω
1744:frequency
1716:π
1705:ω
1701:π
1646:ω
1425:amplitude
1224:
1187:
975:−
910:−
906:⇒
779:−
671:, windup
657:clockwork
623:landmines
597:flintlock
593:wheellock
183:extension
99:Military
3376:Category
3286:Vehicles
3276:Inductor
3266:Resistor
3205:Aerofoil
3195:Windmill
3134:Linkages
2947:Machines
2765:19 April
2740:19 April
2715:19 April
2568:20 March
2522:20 March
2343:"spring"
2305:See also
2263:toasters
2202:Firearms
2140:negative
1517:velocity
1515:and the
716:fastener
689:negating
584:V-spring
575:switches
300:, in an
257:tweezers
230:titanium
218:annealed
211:additive
175:gradient
109:tripwire
3354:Springs
3157:Turbine
2598:Physics
2590:(Video)
2376:Springs
2217:Jewelry
2208:mooring
2163:firmly.
2156:LaCoste
2127:unwinds
1868:tension
1857:elastic
825:is the
747:Physics
708:Spring
661:watches
589:firearm
551:watches
500:Tension
392:tension
247:History
124:elastic
42:Helical
3223:Rudder
3063:Trompe
2998:Clocks
2973:Pulley
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2148:period
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1870:, the
1855:of an
1835:Theory
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954:period
806:where
791:
710:washer
675:, and
665:clocks
577:, and
410:torque
207:ft·lbf
195:torque
120:spring
3315:Robot
3310:Mecha
3261:Diode
3035:pumps
2983:Wedge
2978:Screw
2968:Lever
2358:
2222:Most
2131:could
1872:force
1853:atoms
288:Types
181:. An
179:curve
159:force
152:arrow
148:drawn
3228:Flap
3218:Wing
3213:Sail
3058:Pump
3033:and
2897:2008
2876:2008
2852:2013
2822:ISBN
2807:ISBN
2767:2021
2742:2021
2717:2021
2670:ISBN
2643:ISBN
2612:OCLC
2602:ISBN
2570:2018
2545:help
2524:2018
2455:ISBN
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2274:Toys
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539:cone
452:etc.
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163:rate
105:USSR
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203:rad
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