University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 14 - Periodic Motion - Problems - Exercises - Page 461: 14.38


(a) $k = 3540~N/m$ (b) $T = 0.851~s$ (c) $v_{max} = 0.369~m/s$

Work Step by Step

(a) We can find the force constant of the spring. $kx = mg$ $k = \frac{mg}{x}$ $k = \frac{(65.0~kg)(9.80~m/s^2)}{0.180~m}$ $k = 3540~N/m$ (b) We can find the period of oscillation. $T = 2\pi~\sqrt{\frac{m}{k}}$ $T = 2\pi~\sqrt{\frac{65.0~kg}{3540~N/m}}$ $T = 0.851~s$ (c) We can find the maximum speed. $v_{max} = A~\omega$ $v_{max} = A~\sqrt{\frac{k}{m}}$ $v_{max} = (0.0500~m)~\sqrt{\frac{3540~N/m}{65.0~kg}}$ $v_{max} = 0.369~m/s$
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