Answer
(a) simple harmonic,
(b) $5\ m$,
(c) $4\ sec$,
(d) $\frac{1}{4}\ Hz$.
Work Step by Step
(a) Given $d=5cos(\frac{\pi}{2} t)$, we can describe the motion of the object as simple harmonic,
(b) The maximum displacement from its resting position can be found as $5\ m$,
(c) We can find the period as $p=\frac{2\pi}{\pi/2}=4\ sec$,
(d) The frequency is the reciprocal of the period $f=\frac{1}{p}=\frac{1}{4}\ Hz$.
