Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 8 - Applications of Trigonometric Functions - 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves - 8.5 Assess Your Understanding - Page 553: 8


$y=-4\cdot \cos(4t)$

Work Step by Step

The object starts at the vertical position $y=-a$, and moves up. By definition, the frequency is $\omega=\frac{2\pi}{T}$, hence the function is: $y=-a\cdot \cos(\omega t)=-a\cdot \cos\left(\frac{2\pi}{T}\cdot t\right)$. Here, we have $y=-a\cdot \cos\left(\frac{2\pi}{T} \cdot t\right)=-4\cdot \cos\left(\frac{2\pi}{\frac{\pi}{2}}\cdot t\right)=-4\cdot \cos(4t)$.
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