Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 15 - Oscillations - Problems - Page 439: 61a

Answer

$x_m = \dfrac{F_{m}}{b \omega}$

Work Step by Step

The two angular frequencies equal to each other $$ \omega = \omega_d$$ Put this expression in the given equation to get $x_m$ by \begin{align*} x_{m}&=\frac{F_{m}}{\left[m^{2}\left(\omega_{d}^{2}-\omega^{2}\right)^{2}+b^{2} \omega_{d}^{2}\right]^{1 / 2}}\\ &= \frac{F_{m}}{\left[m^{2}\left(\omega^{2}-\omega^{2}\right)^{2}+b^{2} \omega^{2}\right]^{1 / 2}}\\ &=\boxed{\frac{F_{m}}{b \omega}} \end{align*}
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