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. |
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. |
Wiki Markup |
{table:border=1|frame=void|rules=cols|cellpadding=8|cellspacing=0} {tr:valign=top} {td:width=350|bgcolor=#F2F2F2} {live-template:Left Column} {td} {td} 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} {td} {tr} {table} {live-template:RELATE license} |