A $0\mathrm{.}35$ kg object rests on a frictionless horizontal surface, where it is attached to a massless spring whose $k-$value equals $25\mathrm{.}0\frac{N}{m}.$ Let $x$ be the displacement, where $x=0$ is the equilibrium position and $x>0$ when the spring is stretched. The object is pushed, and the spring compressed, until $x_1=-4\mathrm{.}00cm.$ It then is released from rest and undergoes simple harmonic motion.

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

$\frac{m}{s}$

$($b$)$ How fast is the object moving $($in $\frac{m}{s})$ when the spring is momentarily compressed by $1\mathrm{.}80$ cm $($that is$,$ when $x=-1\mathrm{.}80cm)?$

$$ m$/$s

$($c$)$ How fast is the object moving $($in $\frac{m}{s})$ whenever the spring is extended by $1\mathrm{.}80$ cm $($that is$,$ when passing through $x=+1\mathrm{.}80cm)?$

$\frac{m}{s}$

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

$|x|=$ cm

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