Problem $3(25$ pts$)$

A mousetrap is modeled as a thin bar of length $L$ and mass $m$ that undergoes rapid rotation due to a torsional spring of stiffness $k_1$ acting at its axis of rotation. If the torsional spring is unloaded at $=0$ and released from rest at $=$ determine:

$($a$)$ the angular velocity of the mass center as a function of $,m,$ and $k_t$ and

$($b$)$ the speed of point $A$ as the bar becomes horizontal at $=0.$

Assume that the torsional spring is the primary mechanism leading to motion such that gravity can be neglected.

$T_1{T}_1{V}_1=\frac{1}{2}m{v}_1^2,T_2=\frac{1}{2}m{v}_2^2$