Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 11 - Oscillations and Waves - Problems: 5

Answer

a. $6.5 \times 10^2 N/m$ b. Amplitude is $2.1cm$, frequency is $2.6Hz$

Work Step by Step

a. Find the spring constant by dividing the magnitude of applied force by the displacement. $$k=\frac{F}{x}=\frac{mg}{x}=\frac{(2.4kg)(9.80m/s^2)}{0.036 m}=6.5 \times 10^2 N/m$$ b. Find the oscillation frequency from k and the total mass. $$f=\frac{1}{2 \pi}\sqrt{\frac{k}{m}}=\frac{1}{2 \pi}\sqrt{\frac{653 N/m }{2.4kg}}\approx 2.6Hz$$ The amplitude is the distance that the fish was pulled away from the new equilibrium, or A=2.1 cm.
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