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 - Page 239: 49


$T = 2\pi\sqrt{\frac{m}{k}}$

Work Step by Step

We find: $ \frac{dx}{dt} = A\omega cos \omega t$ Thus, it follows: $ \frac{d^2x}{dt^2} = -A\omega^2 sin \omega t$ Using equation 13.3 and the fact that $ x=Asin\omega t $, we find: $m(-A\omega^2 sin \omega t)=-k Asin\omega t $ Since $ T = \frac{2\pi}{\omega}$, we find: $T = 2\pi\sqrt{\frac{m}{k}}$
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