$2.$ A spring$-$mounted slider moves along a horizontal guide with negligible friction. The horizontal displace

ment of the slider is s$($t$).$ The slider has an initial velocity v$0$ in the s$-$direction $($path direction$)$ as it crosses

the mid$-$position where s $=0$ and t $=0.$ The two springs together exert an opposing force to the motion of

the slider, which gives it an acceleration proportional to the slider displacement, a$($s$)=$ k$2$s$,$ where k is a

constant. Please answer the following questions.

a$)$ Determine the expression for the displacement of the slider s$($t$)$ as a function of time.

b$)$ Determine the expression for the velocity of the slider v$($t$)$ as a function of time.