Spring (device)
Overview
 
A spring is an elastic
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

 object used to store mechanical energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Springs are usually made out of spring steel
Spring steel
Spring steel is a low alloy, medium carbon steel or high carbon steel with a very high yield strength. This allows objects made of spring steel to return to their original shape despite significant bending or twisting.-Grades:...

. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed
Annealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...

 steel and hardened after fabrication. Some non-ferrous metals
Ferrous
Ferrous , in chemistry, indicates a divalent iron compound , as opposed to ferric, which indicates a trivalent iron compound ....

 are also used including phosphor bronze
Phosphor bronze
Phosphor bronze is an alloy of copper with 3.5 to 10% of tin and a significant phosphorus content of up to 1%. The phosphorus is added as deoxidizing agent during melting....

 and titanium
Titanium
Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....

 for parts requiring corrosion resistance and beryllium copper
Beryllium copper
Beryllium copper , also known as copper beryllium, beryllium bronze and spring copper, is a copper alloy with 0.5—3% beryllium and sometimes with other alloying elements. Beryllium copper combines high strength with non-magnetic and non-sparking qualities. It has excellent metalworking, forming...

 for springs carrying electrical current (because of its low electrical resistance).

When a spring is compressed or stretched, the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 it exerts is proportional to its change in length.
Encyclopedia
A spring is an elastic
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

 object used to store mechanical energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Springs are usually made out of spring steel
Spring steel
Spring steel is a low alloy, medium carbon steel or high carbon steel with a very high yield strength. This allows objects made of spring steel to return to their original shape despite significant bending or twisting.-Grades:...

. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed
Annealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...

 steel and hardened after fabrication. Some non-ferrous metals
Ferrous
Ferrous , in chemistry, indicates a divalent iron compound , as opposed to ferric, which indicates a trivalent iron compound ....

 are also used including phosphor bronze
Phosphor bronze
Phosphor bronze is an alloy of copper with 3.5 to 10% of tin and a significant phosphorus content of up to 1%. The phosphorus is added as deoxidizing agent during melting....

 and titanium
Titanium
Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....

 for parts requiring corrosion resistance and beryllium copper
Beryllium copper
Beryllium copper , also known as copper beryllium, beryllium bronze and spring copper, is a copper alloy with 0.5—3% beryllium and sometimes with other alloying elements. Beryllium copper combines high strength with non-magnetic and non-sparking qualities. It has excellent metalworking, forming...

 for springs carrying electrical current (because of its low electrical resistance).

When a spring is compressed or stretched, the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 it exerts is proportional to its change in length. The rate
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

or spring constant of a spring is the change in the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 it exerts, divided by the change in deflection
Deflection (engineering)
In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.The deflection distance of a member under a load is directly related to the slope of the deflected shape of the member under that load and can be calculated by...

 of the spring. That is, it is the gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

 of the force versus deflection curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

. An extension or compression spring has units of force divided by distance, for example lbf/in or N/m. Torsion spring
Torsion spring
A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force it exerts is proportional to the amount it is twisted. There are two types...

s have units of force multiplied by distance divided by angle, such as N·m
Newton metre
A newton metre is a unit of torque in the SI system. The symbolic form is N m or N·m, and sometimes hyphenated newton-metre...

/rad
Radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

 or ft·lbf/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
Additive function
In mathematics the term additive function has two different definitions, depending on the specific field of application.In algebra an additive function is a function that preserves the addition operation:for any two elements x and y in the domain. For example, any linear map is additive...

, as is the compliance of springs in series.

Depending on the design and required operating environment, any material can be used to construct a spring, so long as the material has the required combination of rigidity and elasticity: technically, a wooden bow
Bow (weapon)
The bow and arrow is a projectile weapon system that predates recorded history and is common to most cultures.-Description:A bow is a flexible arc that shoots aerodynamic projectiles by means of elastic energy. Essentially, the bow is a form of spring powered by a string or cord...

 is a form of spring.

History

Simple non-coiled springs were used throughout human history e.g., the bow
Bow (weapon)
The bow and arrow is a projectile weapon system that predates recorded history and is common to most cultures.-Description:A bow is a flexible arc that shoots aerodynamic projectiles by means of elastic energy. Essentially, the bow is a form of spring powered by a string or cord...

 (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of tweezers
Tweezers
Tweezers are tools used for picking up and manipulating objects too small to be easily handled with the human hands. They are probably derived from tongs, pincers, or scissors-like pliers used to grab or hold hot objects since the dawn of recorded history...

 in many cultures. Ctesibius of Alexandria developed a method for making bronze
Bronze
Bronze is a metal alloy consisting primarily of copper, usually with tin as the main additive. It is hard and brittle, and it was particularly significant in antiquity, so much so that the Bronze Age was named after the metal...

 with spring-like characteristics by producing an alloy of bronze with an increased proportion of tin, and then hardening it by hammering after it is cast.

Coiled springs 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.

In 1676 British physicist Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

 discovered the principle behind springs' action, that the force it exerts is proportional to its extension, now called Hooke's law
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

.

Types

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 load, so the spring stretches as the load is applied to it.
  • Compression spring – is designed to operate with a compression load, so the spring gets shorter as the load is applied to it.
  • Torsion spring
    Torsion spring
    A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force it exerts is proportional to the amount it is twisted. There are two types...

     – unlike the above types in which the load is an axial force, the load applied to a torsion spring is a torque
    Torque
    Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

     or twisting force, and the end of the spring rotates through an angle as the load is applied.


They can also be classified based on their shape:
  • Coil spring
    Coil spring
    A Coil spring, also known as a helical spring, is a mechanical device, which is typically used to store energy and subsequently release it, to absorb shock, or to maintain a force between contacting surfaces...

     – this type is made of a coil or helix
    Helix
    A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

     of wire
  • Flat spring – this type is made of a flat or conical shaped piece of metal.
  • Machined spring - this type of spring is manufactured by machining bar stock with a lathe and/or milling operation rather than coiling wire. 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.


The most common types of spring are:
  • Cantilever spring
    Springboard
    A springboard or diving board is used for diving and is a board that is itself a spring, i.e. a linear flex-spring, of the cantilever type....

     – a spring which is fixed only at one end.
  • Coil spring
    Coil spring
    A Coil spring, also known as a helical spring, is a mechanical device, which is typically used to store energy and subsequently release it, to absorb shock, or to maintain a force between contacting surfaces...

     or helical
    Helix
    A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

     spring – a spring (made by winding a wire around a cylinder) and the conical
    Cone (geometry)
    A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...

     spring – these are types of torsion spring
    Torsion spring
    A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force it exerts is proportional to the amount it is twisted. There are two types...

    , because the wire itself is twisted when the spring is compressed or stretched. These are in turn of two types:
    • 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.
      • A volute spring
        Volute spring
        A Volute spring is a compression spring in the form of a cone . Under compression, the coils slide past each other, thus enabling the spring to be compressed to a very short length in comparison to what would be possible with a more conventional helix spring.The shape of the initial spring steel ...

        is a compression spring in the form of a cone, designed so that under compression the coils are not forced against each other, thus permitting longer travel.
    • 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.
  • Hairspring or balance spring
    Balance spring
    A balance spring, or hairspring, is a part used in mechanical timepieces. The balance spring, attached to the balance wheel, controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands...

     – a delicate spiral torsion spring used in watch
    Watch
    A watch is a small timepiece, typically worn either on the wrist or attached on a chain and carried in a pocket, with wristwatches being the most common type of watch used today. They evolved in the 17th century from spring powered clocks, which appeared in the 15th century. The first watches were...

    es, galvanometer
    Galvanometer
    A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an analog electromechanical transducer that produces a rotary deflection of some type of pointer in response to electric current flowing through its coil in a magnetic field. .Galvanometers were...

    s, and places where electricity must be carried to partially-rotating devices such as steering wheel
    Steering wheel
    A steering wheel is a type of steering control in vehicles and vessels ....

    s without hindering the rotation.
  • Leaf spring
    Leaf spring
    Originally called laminated or carriage spring, a leaf spring is a simple form of spring, commonly used for the suspension in wheeled vehicles...

     – a flat spring used in vehicle suspension
    Suspension (vehicle)
    Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...

    s, electrical switch
    Switch
    In electronics, a switch is an electrical component that can break an electrical circuit, interrupting the current or diverting it from one conductor to another....

    es, and bow
    Bow (weapon)
    The bow and arrow is a projectile weapon system that predates recorded history and is common to most cultures.-Description:A bow is a flexible arc that shoots aerodynamic projectiles by means of elastic energy. Essentially, the bow is a form of spring powered by a string or cord...

    s.
  • V-spring – used in antique firearm
    Firearm
    A firearm is a weapon that launches one, or many, projectile at high velocity through confined burning of a propellant. This subsonic burning process is technically known as deflagration, as opposed to supersonic combustion known as a detonation. In older firearms, the propellant was typically...

     mechanisms such as the wheellock
    Wheellock
    A wheellock, wheel-lock or wheel lock, is a friction-wheel mechanism to cause a spark for firing a firearm. It was the next major development in firearms technology after the matchlock and the first self-igniting firearm. The mechanism is so-called because it uses a rotating steel wheel to provide...

    , flintlock
    Flintlock
    Flintlock is the general term for any firearm based on the flintlock mechanism. The term may also apply to the mechanism itself. Introduced at the beginning of the 17th century, the flintlock rapidly replaced earlier firearm-ignition technologies, such as the doglock, matchlock and wheellock...

     and percussion cap
    Percussion cap
    The percussion cap, introduced around 1830, was the crucial invention that enabled muzzleloading firearms to fire reliably in any weather.Before this development, firearms used flintlock ignition systems which produced flint-on-steel sparks to ignite a pan of priming powder and thereby fire the...

     locks.


Other types include:
  • Belleville washer
    Belleville washer
    A Belleville washer, also known as a coned-disc spring, conical spring washer, disc spring, Belleville spring or cupped spring washer, is a type of spring shaped like a washer. It has a frusto-conical shape which gives the washer a spring characteristic. The Belleville name comes from the inventor...

     or Belleville spring – a disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated landmines
    Land mine
    A land mine is usually a weight-triggered explosive device which is intended to damage a target—either human or inanimate—by means of a blast and/or fragment impact....

    ).
  • Constant-force spring
    Constant-force spring
    A constant-force spring is a spring for which the force it exerts over its range of motion is a constant. That is, it does not obey Hooke's law....

     — a tightly rolled ribbon that exerts a nearly constant force as it is unrolled.
  • Gas spring
    Gas spring
    A gas spring is a type of spring that, unlike a typical metal spring, uses a compressed gas, contained in a cylinder and compressed by a piston, to exert a force. Gas springs are used in automobiles, where they are incorporated into the design of struts that support the weight of hatchback doors...

     – a volume of gas which is compressed.
  • Ideal Spring – the notional spring used in physics: it has no weight, mass, or damping losses.
  • Mainspring
    Mainspring
    A mainspring is a spiral torsion spring of metal ribbon that is the power source in mechanical watches and some clocks. Winding the timepiece, by turning a knob or key, stores energy in the mainspring by twisting the spiral tighter. The force of the mainspring then turns the clock's wheels as it...

     – a spiral ribbon shaped spring used as a power source in watch
    Watch
    A watch is a small timepiece, typically worn either on the wrist or attached on a chain and carried in a pocket, with wristwatches being the most common type of watch used today. They evolved in the 17th century from spring powered clocks, which appeared in the 15th century. The first watches were...

    es, clock
    Clock
    A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...

    s, music boxes, windup toy
    Toy
    A toy is any object that can be used for play. Toys are associated commonly with children and pets. Playing with toys is often thought to be an enjoyable means of training the young for life in human society. Different materials are used to make toys enjoyable and cuddly to both young and old...

    s, and mechanically powered flashlights
  • Negator spring
    Constant-force spring
    A constant-force spring is a spring for which the force it exerts over its range of motion is a constant. That is, it does not obey Hooke's law....

     – 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 commonest application is the retracting steel tape rule.
  • Progressive rate coil springs – A coil spring with a variable rate, usually achieved by having unequal pitch
    Pitch
    Pitch may refer to:* Pitch , a viscous substance produced by plants or formed from petroleum* Pitch * sales pitch** elevator pitch, a very short sales pitch such as that made during an elevator ride* Pitch accent-Music and acoustics:...

     so that as the spring is compressed one or more coils rests against its neighbour.
  • Rubber band
    Rubber band
    A rubber band is a short length of rubber and latex formed in the shape of a loop and is commonly used to hold multiple objects together...

     – a tension spring where energy is stored by stretching the material.
  • Spring washer
    Washer (mechanical)
    A washer is a thin plate with a hole that is normally used to distribute the load of a threaded fastener, such as a screw or nut. Other uses are as a spacer, spring , wear pad, preload indicating device, locking device, and to reduce vibration...

     – used to apply a constant tensile force along the axis of a fastener
    Fastener
    A fastener is a hardware device that mechanically joins or affixes two or more objects together.Fasteners can also be used to close a container such as a bag, a box, or an envelope; or they may involve keeping together the sides of an opening of flexible material, attaching a lid to a container,...

    .
  • Torsion spring
    Torsion spring
    A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force it exerts is proportional to the amount it is twisted. There are two types...

     – any spring designed to be twisted rather than compressed or extended. Used in torsion bar
    Torsion beam suspension
    thumb|250px|A front [[VW Beetle]] suspension cross-sectionA torsion bar suspension, also known as a torsion spring suspension or torsion beam suspension, is a general term for any vehicle suspension that uses a torsion bar as its main weight bearing spring...

     vehicle suspension systems.
  • Wave spring – a thin spring-washer into which waves have been pressed.

Physics

Hooke's law

As long as they are not stretched or compressed beyond their elastic limit, most springs obey Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length:
where
x is the displacement vector – the distance and direction in which the spring is deformed
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.


Coil spring
Coil spring
A Coil spring, also known as a helical spring, is a mechanical device, which is typically used to store energy and subsequently release it, to absorb shock, or to maintain a force between contacting surfaces...

s 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 with displacement.

Simple harmonic motion

Since force is equal to mass, m, times acceleration, a, the force equation for a spring obeying Hooke's law
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

 looks like:
The mass of the spring is assumed small in comparison to the mass of the attached mass and is ignored. Since acceleration is simply the second derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

 of x with respect to time,
This is a second order linear differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

 for the displacement as a function of time. Rearranging:
the solution of which is the sum of a sine
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

 and cosine:
and are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with (zero initial position with some positive initial velocity) is displayed in the image on the right.

Theory

In classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

, a spring can be seen as a device that stores potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

, specifically elastic potential energy, by straining the bonds between the atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s of an elastic
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

  material.

Hooke's law
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

 of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension
Tension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...

, the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 used to stretch it. Similarly, the contraction (negative extension) is proportional to the compression (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
Tensile strength
Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...

, 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 of one variable approximates a quadratic function
Quadratic function
A quadratic function, in mathematics, is a polynomial function of the formf=ax^2+bx+c,\quad a \ne 0.The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis....

 when examined near enough to its minimum point; and therefore the force — which is the derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

 of energy with respect to displacement — will approximate a linear function
Linear function
In mathematics, the term linear function can refer to either of two different but related concepts:* a first-degree polynomial function of one variable;* a map between two vector spaces that preserves vector addition and scalar multiplication....

.

Force of fully compressed spring


where
E – Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

d – spring wire diameter
L – free length of spring
n – number of active windings
– Poisson ratio
D – spring outer diameter

Zero-length springs

"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. Obviously a coil spring cannot contract to zero length because at some point the coils will touch each other and the spring will not be able to shorten any more. Zero length springs are made by manufacturing a coil spring with built-in tension, 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, zero length springs 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 spring with zero length 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 pendulum with very long period. Long-period pendulums enable seismometer
Seismometer
Seismometers are instruments that measure motions of the ground, including those of seismic waves generated by earthquakes, volcanic eruptions, and other seismic sources...

s to sense the slowest waves from earthquakes. The LaCoste suspension with zero-length springs is also used in gravimeter
Gravimeter
A gravimeter or gravitometer is an instrument used in gravimetry for measuring the local gravitational field of the Earth. A gravimeter is a type of accelerometer, specialized for measuring the constant downward acceleration of gravity, which varies by about 0.5% over the surface of the Earth...

s because it is very sensitive to changes in gravity. Springs for closing doors are often made to have roughly zero length so that they will exert force even when the door is almost closed, so it will close firmly.

Uses

  • Balance spring
    Balance spring
    A balance spring, or hairspring, is a part used in mechanical timepieces. The balance spring, attached to the balance wheel, controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands...

    s mechanical timepieces
  • Buckling spring
    Buckling spring
    A buckling spring is a type of keyswitch mechanism, popularized by IBM's keyboards for the PC, PC/AT, 5250/3270 terminals, PS/2, and other systems. It was used by IBM's Model F keyboard, and the more common Model M. It is described in ....

     keyboards
  • In CD players
    Compact disc player
    A Compact Disc player , or CD player, is an electronic device that plays audio Compact Discs. CD players are often a part of home stereo systems, car audio systems, and personal computers. They are also manufactured as portable devices...

  • Inside a pen
    Pen
    A pen is a device used to apply ink to a surface, usually paper, for writing or drawing. Historically, reed pens, quill pens, and dip pens were used, with a nib of some sort to be dipped in the ink. Ruling pens allow precise adjustment of line width, and still find a few specialized uses, but...

  • Mattress
    Mattress
    A mattress is a manufactured product to sleep or lie on, consisting of resilient materials and covered with an outer fabric or ticking. In the developed world it is typically part of a bed set and is placed upon a foundation....

  • Pogo Stick
    Pogo stick
    A pogo stick is a device for jumping off the ground in a standing position with the aid of a spring, used as a toy or exercise equipment. It consists of a pole with a handle at the top and footrests near the bottom, and a spring located somewhere along the pole...

  • Slinky
    Slinky
    Slinky or "Lazy Spring" is a toy consisting of a helical spring that stretches and can bounce up and down. It can perform a number of tricks, including traveling down a flight of steps end-over-end as it stretches and re-forms itself with the aid of gravity and its own momentum.-History:The toy was...

  • Trampoline
    Trampoline
    A trampoline is a device consisting of a piece of taut, strong fabric stretched over a steel frame using many coiled springs. People bounce on trampolines for recreational and competitive purposes....

  • Vehicle suspension
  • Whammy bar

External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK