Problem $17\mathrm{.}039-$ The velocity of a constrained rod subject to spring tension and gravity

The ends of a $8$ lb rod $AB$ are constrained to move along slots cut in a vertical plate as shown. A spring of constant $k=3l\frac{b}{?}$ in $.$ is attached to end $A$ in such a way that its tension is zero when $=0.$ If the rod is released from rest when $=50,$ determine the angular velocity of the rod and the velocity of end $B$ when $=0.($Round the final answers to three decimal places.$)$

The angular velocity of the rod is $$ rad$/$s $($Click to select$).$

The velocity of end $B$ when $=0$ is $f\frac{t}{s}($Click to select$)$ v$.$