A slender $7\mathrm{.}5-lb$ rod can rotate in a vertical plane about a pivot at $B.$ A spring of constant $k=33l\frac{b}{f}t$ and of unstretched length $4\mathrm{.}2$ in $.$ is attached to the rod as shown. Knowing that the rod is released from rest in the position shown, determine its angular velocity $(ra\frac{d}{s})$ after it has rotated hrough $90$

$7\mathrm{.}57$

$17\mathrm{.}37$

$16\mathrm{.}41$

$13\mathrm{.}72$