Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 13 - Exercises and Problems - Page 238: 19


a)$ x(t) = (.125m)cos(42.0t)$ b)$ x(t) = (2.15 cm)sin(4.63t)$

Work Step by Step

Here, we know that we must use the equation: $$x(t)=Acos( \omega t + \phi)$$ Where omega is the angular frequency, A is the amplitude, and phi is the phase constant. We know: $$ \omega = 2 \pi f$$ a) $ \omega = 2 \pi (6.68 Hz)$ b) $ \omega = 2 \pi (4.63 Hz)$ Using these two results, we get the answer: a)$ x(t) = (.125m)cos(42.0t)$ b)$ x(t) = (2.15 cm)sin(4.63t)$ Note, the fact that one function is a cosine function while the other is the sine function reflects the phase difference.
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