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

Published by Pearson

Chapter 15 - Oscillations - Exercises and Problems: 33

Answer

$\tau = 10.0~s$

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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