## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.5 Harmonic Motion - 4.5 Exercises - Page 185: 11b

#### Answer

Amplitude=2 Period$=\frac{\pi}{2}$ sec Frequency$=\frac{2}{\pi}$ rotations per sec

#### Work Step by Step

Since the particle moves uniformly around a circle of radius $2$ units, its amplitude $a$ is $2$. Also, it is given that the angular speed $w$ is 4 radians per second. As we are interested in the displacement $s(t)$ of the particle from the equilibrium position, the equation is: $s(t)=a\sin wt$ $s(t)=2\sin 4t$ We know that the amplitude is 2. In addition, $w$ can be used to find the period: Period$=\frac{2\pi}{w}$ Period$=\frac{2\pi}{4}$ Period$=\frac{\pi}{2}$ sec Since frequency is the reciprocal of period, frequency$=\frac{2}{\pi}$ rotations per sec.

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