Simple harmonic motion

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Simple harmonic motion

An object moves in simple harmonic motion whenever its acceleration is proportional to its position and is oppositely directed to the displacement from equilibrium:

\[\mathbf{a} \propto -\Delta \mathbf{r}.\]

Example: a mass-spring system on a horizontal frictionless surface

\[F_x = -k x\]

\[F_x = m a\]

\[a = -\frac{k}{m} x\]

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