Chapter 4.5, Problem 24PS

Each of the following graphs shows at least one complete cycle of the graph of an equation containing a trigonometric function. In each case, find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

Simple Harmonic Motion. As discussed earlier in Problem Set 4.2, any object or quantity that is moving with a periodic sinusoidal oscillation is said to exhibit simple harmonic motion. This motion can be modeled by the trigonometric function $y=A\sin \left(\omega t\right)$ or

$y=A\cos \left(\omega t\right)$ where A and $\omega$ are constants. The frequency given by

$f=1/period$ represents the number of cycles (or oscillations that are completed per unit time. The unit used to describe frequency is the Hertz, where $1\text{Hz}=1$ cycle per second.