Problem $4\mathrm{.}10$

A slender $4kg$ rod can rotate in a vertical plane about a

pivot at $B.$ A spring having a constant of $k=400\frac{N}{m}$ and

unstretched length of $l=150mm$ is attached to the rod as

shown. The rod is released from rest in the position shown.

Determine:

a$)$ the angular velocity of the rod after it has rotated

through $90.$

b$)$ the reactions at point $B$ after the rod has rotated

through $90.$

$($a$)=11\mathrm{.}1ra\frac{d}{s}$

$($b$),B_x=57\mathrm{.}2N,B_y=18\mathrm{.}9arr$