$15\mathrm{.}2\mathrm{.}2.$ A steel ball is hung from a vertical ideal spring where it oscillates in simple harmonic motion with an amplitude of $0\mathrm{.}157$ m and an angular frequency of $ra\frac{d}{s}.$ Which one of the following expressions represents the acceleration, in $\frac{m}{s^2},$ of the ball as a function of time?

a$)a=-1\mathrm{.}55cos(t)$

b$)a=-1\mathrm{.}55co{s}^2(t)$

c$)a=-0\mathrm{.}157cos(t)$

d$)a=-0\mathrm{.}493co{s}^2(t)$

e$)a=-0\mathrm{.}493cos(t)$