A small box with mass $0\mathrm{.}5$kg is attached to a spring $(200$ N$/$m$)$ and oscillates left and right with no

dissipative forces. At time t $=0,$ the box is $25$cm to the right of its equilibrium position and moving left

with a speed of $3$m$/$s$.$

$($a$)$ What is the maximum distance to the right of its equilibrium position the box will reach?

$($b$)$ What is the maximum speed the box will reach as it oscillates?

$($c$)$ What is the period of the box$$s oscillations?

$($d$)$ What is the maximum magnitude of acceleration the box will experience?