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: 11



Work Step by Step

The natural period of vibration can be determined as follows: $\omega_n=\sqrt{\frac{K}{m}}$ $\omega_n=\sqrt{\frac{mg}{m\delta_{st}}}$ $\implies \omega_n=\sqrt{\frac{g}{\delta_{st}}}$ We plug in the known values to obtain: $\omega_n=\sqrt{\frac{28.32}{\frac{18in}{12in/ft}}}$ $\implies \omega_n=4.3359rad/s$ Now $T=\frac{2\pi}{\omega_n}$ $\implies T=\frac{2\pi}{4.3359}$ $\implies T=1.45s$
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