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: 15



Work Step by Step

Since the general equation is $s(t)=a\sin w t$, we first need to compare $s(t)=a\sin w t$ with $s(t)=a\sin \sqrt \frac{k}{m}t$ to find the value of $w$. Comparing, we find that $w=\sqrt \frac{k}{m}$. We know that $w$ and the period are linked through the formula: Period$=\frac{2\pi}{w}$ We substitute $w=\sqrt \frac{k}{m}, k=4$ and Period$=1$ into the formula and solve: $1=\frac{2\pi}{\sqrt \frac{k}{m}}$ $1=\frac{2\pi}{\sqrt \frac{4}{m}}$ $\sqrt \frac{4}{m}=2\pi$ $\frac{4}{m}=4\pi^{2}$ $\frac{4}{4\pi^{2}}=m$ $m=\frac{1}{\pi^{2}}$ Therefore, the mass must be $\frac{1}{\pi^{2}}$.
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