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A restoring force is

Excerpt

a A force operating directed opposite the direction of displacement of a mass, regardless of its direction

, that grows with displacement from this position and

from some equilibrium position that acts to restore the mass to

its stable

the equilibrium location. The

term is almost always used of a force

most commonly analyzed case is a restoring force which has a magnitude linearly proportional to the displacement from equilibrium, leading

to periodic motion

to Simple Harmonic Motion.

Utility of the Linear Approximation

The mathematics of Taylor series expansions can be used to show that the motion of any system subject to a net restoring force will be accurately described by the Simple Harmonic Motion model for very small displacements from equilibrium.

Note

As with any series expansion, the term "very small" must be defined for a given system according to the parameters of the relevant force law and the desired accuracy of the description.