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The force responsible for restoring original size and shape is called the restoring force. [1] [2] An example is the action of a spring. An idealized spring exerts a force proportional to the amount of deformation of the spring from its equilibrium length, exerted in a direction oppose the deformation.
Hooke's law for a spring is also stated under the convention that F s is the restoring force exerted by the spring on whatever is pulling its free end. In that case, the equation becomes F s = − k x {\displaystyle F_{s}=-kx} since the direction of the restoring force is opposite to that of the displacement.
However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Mathematically, F = − k x , {\displaystyle \mathbf {F} =-k\mathbf {x} ,} where F is the restoring elastic force exerted by the spring (in SI units: N ), k is the spring constant ( N ·m −1 ), and x is the ...
When a spring is stretched or compressed by a mass, the spring develops a restoring force. Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length: F ( t ) = − k x ( t ) , {\displaystyle F(t)=-kx(t),} where F is the force, k is the spring constant, and x is the ...
is the resulting force vector – the magnitude and direction of the restoring force the spring exerts 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
This discussion applies the following simplifications: the spring itself is taken as being weightless, and the spring is taken as being a perfect spring; the restoring force increases in a linear way as the spring is stretched out. That is, the restoring force is exactly proportional to the distance from the center of rotation.
The restoring force provided by the nonlinear spring is then +. When α > 0 {\displaystyle \alpha >0} and β > 0 {\displaystyle \beta >0} the spring is called a hardening spring . Conversely, for β < 0 {\displaystyle \beta <0} it is a softening spring (still with α > 0 {\displaystyle \alpha >0} ).
The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a restoring force which grows stronger the further the system deviates from equilibrium. In the case of the spring-mass system, Hooke's law states that the restoring force of a spring is: =