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 186: 20a


$s(t)=-2\cos 6\pi t$

Work Step by Step

The general equation regarding the oscillation of a weight attached to a spring is $s(t)=a\cos wt$. Since the weight is first pulled down and then released, the equation becomes $s(t)=-a\cos wt$. Also, as the weight is pulled down 2 inches, the amplitude of the motion is 2. The equation therefore becomes $s(t)=-2\cos wt$. Now we need to find $w$. Since the period is $\frac{1}{3}$, we can use the following formula to find $w$: Period$=\frac{2\pi}{w}$ $1/3=\frac{2\pi}{w}$ $w=\frac{2\pi}{1/3}$ $w=6\pi$ Therefore, the model that gives the position of the weight at time $t$ is $s(t)=-2\cos 6\pi t$.
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