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A force directed opposite the displacement of a mass from some equilibrium position that acts to restore the mass to the equilibrium location. The most commonly analyzed case is a restoring force which has a magnitude linearly proportional to the displacement from equilibrium, leading 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.
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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. |