Problem $17\mathrm{.}018-$ The angular velocity of a pivoting rod$-$spring system

A slender $9-$lb rod can rotate in a vertical plane about a pivot at $B.$ A spring of constant $k=21l\frac{b}{f}t$ and of unstretched length $6$ in$.$ is attached to the rod as shown in the figure. Knowing that the rod is released from rest in the position shown in the figure, determine its angular velocity after it has rotated through $90.$

The angular velocity after it has rotated through $90$ is rad$/$s