Nannie Mack

2021-08-12

An object moves in simple harmonic motion, where t is measured in seconds and d in inches. Help to find the following: a. the maximum displacement, b. the frequency, c. the time required for one cycle, d. the phase shift of the motion.
$d=-2\mathrm{sin}\left(\pi t/4+\pi /2\right)$

broliY

a. maximum displacement is $|a|=2,$
b. the frequency is $f=\frac{\omega }{2\pi }=\frac{\frac{\pi }{4}}{2\pi }=\frac{1}{8}$
c. The time required for one cycle, period is $=\frac{1}{f}=8$
d. The phase shift $=\frac{-\frac{\pi }{2}}{\frac{\pi }{4}}=-2$
$|a|=2.f=\frac{1}{8}$. period = 8. phase shift = -2

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