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: 16

Answer

(a) $k = 24.5~N/m$ (b) $T = 0.898~s$ (c) $v_{max} = 0.700~m/s$ The maximum speed occurs as the mass passes through the equilibrium position.

Work Step by Step

(a) We can find the spring constant as: $kx = mg$ $k = \frac{mg}{x}$ $k = \frac{(0.500~kg)(9.80~m/s^2)}{0.20~m}$ $k = 24.5~N/m$ (b) We can find the period of oscillation as: $T = 2\pi~\sqrt{\frac{m}{k}}$ $T = 2\pi~\sqrt{\frac{0.500~kg}{24.5~N/m}}$ $T = 0.898~s$ (c) We can find the maximum speed as: $v_{max} = A~\omega$ $v_{max} = A~\sqrt{\frac{k}{m}}$ $v_{max} = (0.100~m)~\sqrt{\frac{24.5~N/m}{0.500~kg}}$ $v_{max} = 0.700~m/s$ The maximum speed occurs as the mass passes through the equilibrium position.
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.