Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 13 - Exercises and Problems: 59

Answer

$\sqrt{\frac{k_1+k_2}{m}}$

Work Step by Step

We use Newton's second law to find: $m \frac{d^2x}{dt^2}=F \\ m \frac{d^2x}{dt^2}= -k_1x-k_2x \\ m \frac{d^2x}{dt^2}= -x(k_1+k_2) $ We see from this equation that k is equal to the sum of $k_1$ and $k_2$, so it follows: $ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{k_1+k_2}{m}} $
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