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 - Problems - Page 437: 24

Answer

The frequency of the oscillations is $~~18.2~Hz$

Work Step by Step

We can find the equivalent spring constant $K$ of the two springs in combination. When the springs are stretched a total distance of $x$ then each spring is stretched a distance of $\frac{x}{2}$ We can find $K$: $Kx = k~\frac{x}{2}$ $Kx = (6430~N/m)(\frac{x}{2})$ $k = 3215~N/m$ We can find the frequency of the oscillations: $f = \frac{1}{2\pi}~\sqrt{\frac{K}{m}}$ $f = \frac{1}{2\pi}~\sqrt{\frac{3215~N/m}{0.245~kg}}$ $f = 18.2~Hz$ The frequency of the oscillations is $~~18.2~Hz$
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