Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.5 Harmonic Motion - 4.5 Exercises - Page 179: 6

Answer

$s(t) = 0.11~cos~220\pi t$ We can see a sketch of the graph of $s(t)$ in the window $[0,0.05]$ by $[-0.3, 0.3]$

Work Step by Step

$s(t) = a~cos~\omega t$ $s(0) = 0.11$ and it is given in the question that $s(0)$ is the maximum displacement. Therefore, $a = 0.11$ We can find $\omega$: $\omega = 2\pi~F = (2\pi)(110) = 220\pi$ We can write the expression for $s(t)$: $s(t) = 0.11~cos~220\pi t$ We can see a sketch of the graph of $s(t)$ in the window $[0,0.05]$ by $[-0.3, 0.3]$
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