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h1. Restoring Force

{excerpt}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].{excerpt}

h3. 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 paramters of the force law and the desired accuracy of the analysis.{note}

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