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# Chapter 10: Periodic Motion

Difficulty Level: At Grade Created by: CK-12

Periodic motion is any motion that repeats itself.  This chapter covers a particular case of such called simple harmonic motion - for motion back and forth in a straight line such as a pendulum.  The properties of simple harmonic motion include the basics of wave properties.

Chapter Outline

### Chapter Summary

1. The projection of uniform circular motion onto a straight line is called simple harmonic motion(SHM); it is the simplest form of periodic motion.
2. An object performing SHM must have a restoring force upon it that seeks to return it to its equilibrium position which is directly proportional to the object’s displacement; that is F=kx\begin{align*}F=-kx\end{align*} where the negative sign indicates that the restoring force and displacement are oppositely directed and k\begin{align*}k\end{align*}is a constant of proportionality.
3. The period T\begin{align*}T\end{align*} for a mass m\begin{align*}m\end{align*} on a spring is T=2πmk\begin{align*} T=2 \pi \sqrt{\frac{m}{k}}\end{align*} where the spring is constant is k\begin{align*}k\end{align*}.
4. The frequency is f=1T\begin{align*}f=\frac{1}{T}\end{align*} or f=12πkm\begin{align*}f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\end{align*}
5. The period T\begin{align*}T\end{align*} of a simple pendulum of length \begin{align*}L\end{align*} is \begin{align*}T=2 \pi \sqrt{\frac{L}{g}}\end{align*} where the gravitational acceleration is \begin{align*}g\end{align*}.
1. Waves transmit energy but not mass.
6. Longitudinal waves occur when vibrations are parallel to wave direction.
7. Transverse waves occur when vibrations are perpendicular to the wave direction.
8. Reflection occurs when waves bounce off one medium back into the medium they originated from.
9. Refraction occurs when waves bend entering one medium from the other.
10. Diffraction occurs when waves spread out and when waves bend behind objects.

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Jun 10, 2014