The block is pushed, and the spring compressed, until $x_i=-4\mathrm{.}00cm.$ It then is released from rest and undergoes simple harmonic motion.

$($a$)$ What is the block's maximum speed $($in $\frac{m}{s})$ after it is released?

$\frac{m}{s}$

$($b$)$ How fast is the block moving $($in $\frac{m}{s})$ when the spring is momentarily compressed by $2\mathrm{.}30cm($that is$,$ when $x=-2\mathrm{.}30cm)?$

$\frac{m}{s}$

$($c$)$ How fast is the block moving $($in $\frac{m}{s})$ whenever the spring is extended by $2\mathrm{.}30cm($that is$,$ when passing through $x=+2\mathrm{.}30cm)?$

$\frac{m}{s}$

$($d$)$ Find the magnitude of the displacement $($in $cm)$ at which the block moves with one$-$half of the maximum speed.

$|x|=,cm$