$15\mathrm{.}7($Average$)$ A particle undergoing SHM about $x=0$ travels a total distance of $40$ cm in each cycle. Its maximum acceleration is $3\mathrm{.}6\frac{m}{s^2}.$ At $t=0,$ it is at its maximum positive displacement.

$($a$)$ Find $x(t).$

$($b$)$ Find the first two times when the particle passes through the origin.

$($c$)$ If the particle has a mass $m=1kg,$ what is the