Question $5$

$21\mathrm{.}21$ A slender bar of mass $m$ and length $l$ is pinned to a fixed support as shown. A torsional spring of constant $k$ attached to the ba at the support is un$-$stretched when the bar is vertical. Derive an equation governing small vibrations of the bar by using Energy method from its vertical equilibrium position..

Hint: The potential energy in the spring $[$:$=\frac{1}{2}k{}^2\}$