A $0\mathrm{.}48-kg$ object connected to a light spring with a force constant of $21\mathrm{.}6\frac{N}{m}$ oscillates on a frictionless horizontal surface. The spring is

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

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

$\frac{m}{s}$

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

$\frac{m}{s}$

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