# 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

- The projection of uniform circular motion onto a straight line is called
*simple harmonic motion*(SHM); it is the simplest form of periodic motion. - 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 \begin{align*}F=-kx\end{align*}
F=−kx where the negative sign indicates that the restoring force and displacement are oppositely directed and \begin{align*}k\end{align*}k is a constant of proportionality. - The period \begin{align*}T\end{align*}
T for a mass \begin{align*}m\end{align*}m on a spring is \begin{align*} T=2 \pi \sqrt{\frac{m}{k}}\end{align*}T=2πmk−−−√ where the spring is constant is \begin{align*}k\end{align*}k . - The frequency is \begin{align*}f=\frac{1}{T}\end{align*}
f=1T or \begin{align*}f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\end{align*}f=12πkm−−−√ - The period \begin{align*}T\end{align*}
T of a simple pendulum of length \begin{align*}L\end{align*}L is \begin{align*}T=2 \pi \sqrt{\frac{L}{g}}\end{align*} where the gravitational acceleration is \begin{align*}g\end{align*}.- Waves transmit energy but not mass.

- Longitudinal waves occur when vibrations are parallel to wave direction.
- Transverse waves occur when vibrations are perpendicular to the wave direction.
- Reflection occurs when waves bounce off one medium back into the medium they originated from.
- Refraction occurs when waves bend entering one medium from the other.
- Diffraction occurs when waves spread out and when waves bend behind objects.

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Description

Covers motion back and forth in a straight line such as a pendulum, including wave properties and phenomena.

Difficulty Level:

At Grade
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Date Created:

Jun 10, 2014
Last Modified:

Mar 31, 2016
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