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 - Page 403: 28

Answer

See the detailed answer below.

Work Step by Step

First, we need to find the period of this pendulum which is given by $$T=2\pi\sqrt{\dfrac{L}{g}}\tag 1$$ Now we need to find the number of full oscillations from 8 am to 12 pm which is 4 hours. $$N=\dfrac{t}{T}$$ Plugging from (1); $$N=\dfrac{t}{2\pi\sqrt{\dfrac{L}{g}}}$$ Plugging the known; $$N=\dfrac{(4\times 3600)}{2\pi\sqrt{\dfrac{15}{9.8}}}$$ $$N=\color{red}{\bf1852}\;\rm oscillation$$ Now we need to find the amplitude after these 4 hours which is given by $$A=A_0e^{-t/2\tau}$$ where $\tau=\dfrac{m}{b}$ $$A=1.5e^{-bt/2m}$$ Plugging the known; $$A=1.5e^{\left[\frac{-(0.010)(4\times 3600)}{2(110)}\right]}$$ $$A=\color{red}{\bf0.78}\;\rm m$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.