Two $4-kg$ sliders A and $B$ are connected by a massless

rod of length $l=1m,$ as shown in the figure. When

$x=0,$ a linear impulse of $2$ N $-$s is applied on the

slider $B$ in the positive $x-$direction, resulting in an

initial velocity $v_0.$ The motion occurs in the vertical

plane $(\{$:$g=9\mathrm{.}81\frac{m}{s^2}).$ A linear spring is connected

to the slider $B,$ as shown in the figure. The spring

is unstretched when $x=0.($a$)$ Using the principles

of work$-$energy, determine the the maximum velocity

of the slider $B.$ Also, $($b$)$ using the given $x-y$

coordinate system, determine the angular velocity

vector vec$()$ of the connecting rod, when slider $B$ reaches

its maximum velocity. The spring constant $k=10$

$\frac{N}{m}.$ Assume that friction is negligible and the

motion is restricted to $y>0.$

$(16+6)$