A $0\mathrm{.}50-$kg object connected to a light spring with a force constant of $19\mathrm{.}4$ N$/$m oscillates on a frictionless horizontal surface. The spring is compressed $4\mathrm{.}0$ cm and released from rest.

$($a$)$ Determine the maximum speed of the object.

m$/$s

$($b$)$ Determine the speed of the object when the spring is compressed $1\mathrm{.}5$ cm$.$

m$/$s

$($c$)$ Determine the speed of the object as it passes the point $1\mathrm{.}5$ cm from the equilibrium position.

m$/$s

$($d$)$ For what value of x does the speed equal one$-$half the maximum speed?

m