An object moves in simple harmonic motion, where t is measured in seconds and d

Lipossig 2021-10-15 Answered

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.
\(d = −2\sin (\pi t/4 + π/2)\)

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Answered 2021-10-16 Author has 13457 answers
Maximum displacement , \(\displaystyle{\left|{a}\right|}={2},\)
Frequency, \(\displaystyle{f}=\frac{\omega}{{{2}\pi}}=\frac{{\frac{\pi}{{4}}}}{{{2}\pi}}=\frac{{1}}{{8}}\)
Time required for one cycle, period \(\displaystyle=\frac{{1}}{{f}}={8}\)
Phase shift \(\displaystyle=\frac{{-\frac{\pi}{{2}}}}{{\frac{\pi}{{4}}}}=-{2}\);
\(\displaystyle{\left|{a}\right|}={2};{f}=\frac{{1}}{{8}}\); period = 8; phase shift = -2
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