Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 14 - Oscillations - Exercises and Problems: 19

Answer

(a) The period is 4.00 seconds. (b) The period is 5.66 seconds. (c) The period is 2.83 seconds. (d) The period is 4.00 seconds.

Work Step by Step

We can find an expression for the original period. $T = 2\pi~\sqrt{\frac{L}{g}} = 4.00~s$ (a) Since the period does not depend on the mass, the period is still 4.00 seconds. (b) $T' = 2\pi~\sqrt{\frac{2L}{g}}$ $T' = \sqrt{2}\times ~2\pi~\sqrt{\frac{L}{g}}$ $T' = \sqrt{2}~T$ $T' = \sqrt{2}~(4.00~s)$ $T' = 5.66~s$ (c) $T' = 2\pi~\sqrt{\frac{L/2}{g}}$ $T' = \frac{1}{\sqrt{2}}\times ~2\pi~\sqrt{\frac{L}{g}}$ $T' = \frac{1}{\sqrt{2}}~T$ $T' = \frac{1}{\sqrt{2}}~(4.00~s)$ $T' = 2.83~s$ (d) Since the period does not depend on the amplitude, the period is still 4.00 seconds.
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