Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 11 - Oscillations and Waves - Problems - Page 322: 8

Answer

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Work Step by Step

a. Assume that down is the positive direction. We are told k = 305 N/m, A = 0.280m, and m = 0.235 kg. We calculate $\omega = \sqrt{k/m}=36.026\;rad/s$. The mass has zero displacement and a positive velocity at t = 0, so the equation is a sine function. $$y(t) = (0.280m)sin(36.0\;rad/s)(t))$$ b. The period of oscillation is $T=2 \pi/\omega = 0.1744\;s$. The spring will first reach its longest extension at T/4. It will return there 1 period later, 2 periods later, etc. $$t_{longest}=\frac{T}{4}+nT$$ Where n = 0, 1, 2, 3, … The spring will first reach its longest extension at 3T/4. It will return there 1 period later, 2 periods later, etc. $$t_{shortest}=\frac{3T}{4}+nT$$ Where n = 0, 1, 2, 3, …
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