Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 15 - Oscillations - Exercises and Problems - Page 416: 33


$\tau = 10.0~s$

Work Step by Step

We can use the following equation to find the time constant $\tau$: $x(t) = A~e^{\frac{-t}{\tau}}$ $0.368~A = A~e^{\frac{-10~s}{\tau}}$ $0.368 = e^{\frac{-10~s}{\tau}}$ $ln(0.368) = ln(e^{\frac{-10~s}{\tau}})$ $ln(0.368) = \frac{-10~s}{\tau}$ $\tau = \frac{-10~s}{ln(0.368)}$ $\tau = 10.0~s$
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