Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 7 - Applications of Trigonometric Functions - Section 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves - 7.5 Assess Your Understanding - Page 574: 12


$ - 4 \ \sin( 4t)$

Work Step by Step

The object starts at the vertical position $y=0$, and moves in the downward direction. The frequency is given by: $\omega=\dfrac{2\pi}{T}$ So, the function has the form $y=-a \ \sin(\omega t)=-a \ \sin(\dfrac{2\pi}{T} t)$. Here, $y=- 4 \times \sin (\dfrac{2\pi}{\frac{\pi}{2}} \times t)= - 4 \ \sin( 4t)$
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