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

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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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