Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 15 - Oscillations - Questions - Page 435: 11d

Answer

Greater than the first experiment.

Work Step by Step

Kinetic energy is defined as $K=\frac{1}{2}mv^2$. The maximum velocity of a undamped mass-spring system is equal to $A \omega$, where $\omega$ is equal to $2\pi f$. Redefining $f$ as $\frac{1}{T}$ leaves $v_{max}=\frac{2\pi A}{T}$ and substituting max velocity into kinetic energy leaves $$K_{max}=\frac{2{\pi}^{2}Am}{T^2}$$ So, as $m$ and $T$ remain constant over the two experiments while the amplitude is greater for experiment 2 than experiment 1. As $A$ increases, maximum kinetic energy increases. Therefore, the maximum kinetic energy is greater in experiment 2 than experiment 1.
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