Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 22 - Vibrations - Section 22.1 - Undamped Free Vibration - Problems - Page 652: 4


$13.9rad/s$ $0.452s$

Work Step by Step

We can determine the natural frequency and the period of vibration as follows: $K=\frac{W}{\delta_{st}}$ $\implies K=\frac{20}{\frac{4in}{12in/ft}}=60lb/ft$ Now $\omega_n=\sqrt{\frac{K}{m}}$ We plug in the known values to obtain: $\omega_n=\sqrt{\frac{60}{\frac{10}{32.2}}}=13.9rad/s$ and the period of vibration is given as $T=\frac{2\pi}{\omega}$ $\implies T=\frac{2\pi}{13.9}$ $\implies T=0.452s$
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