Editing Simple harmonic motion (section)

{{Short description|To-and-fro periodic motion in science and engineering}}
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[[File:Simple Harmonic Motion Orbit.gif|thumb|upright=1.5|Simple harmonic motion shown both in real space and [[phase space]]. The [[orbit (dynamics)|orbit]] is [[periodic function|periodic]]. (Here the [[velocity]] and [[position (vector)|position]] axes have been reversed from the standard convention to align the two diagrams)]]
{{Classical mechanics}}

In [[mechanics]] and [[physics]], '''simple harmonic motion''' (sometimes abbreviated as '''{{abbr|SHM|simple harmonic motion}}''') is a special type of [[periodic function|periodic]] [[motion]] an object experiences by means of a [[restoring force]] whose magnitude is directly [[proportionality (mathematics)|proportional]] to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an [[oscillation]] that is described by a [[sinusoid]] which continues indefinitely (if uninhibited by [[friction]] or any other [[dissipation]] of [[energy]]).<ref>{{cite web |date=2024-09-30 |title=Simple harmonic motion {{!}} Formula, Examples, & Facts {{!}} Britannica |website=britannica.com |language=en |url=https://www.britannica.com/science/simple-harmonic-motion |access-date=2024-10-11}}</ref>

Simple harmonic motion can serve as a [[mathematical model]] for a variety of motions, but is typified by the oscillation of a [[mass]] on a [[spring (device)|spring]] when it is subject to the linear [[elasticity (physics)|elastic]] restoring force given by [[Hooke's law]]. The motion is [[sinusoidal]] in time and demonstrates a single [[resonance|resonant]] frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a [[pendulum|simple pendulum]], although for it to be an accurate model, the [[net force]] on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see [[small-angle approximation]]). Simple harmonic motion can also be used to model [[molecular vibration]].

Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of [[Fourier analysis]].