Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

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


Amplitude=2 Period$=\pi$ sec frequency$=\frac{1}{\pi}$ 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 2 cycles per second. As we are interested in the displacement $s(t)$ of the particle from the equilibrium position, the equation is: $s(t)=a\sin wt$ $s(t)=2\sin 2t$ We know that the amplitude is 2. In addition, $w$ can be used to find the period: Period$=\frac{2\pi}{w}$ Period$=\frac{2\pi}{2}$ Period$=\pi$ sec Since frequency is the reciprocal of period, frequency$=\frac{1}{\pi}$ rotations per sec
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