Can you do the full solution and please show how to substitute the inital conditions and give the final answer.

Determine the boundary conditions, and show how would derive the frequency equation of

longitudinal vibration of a uniform rod where $K1=K2=k.$

$u(x,t)=(A_{1}sin\frac{}{c}x+A_{2}cos\frac{}{c}x)q(t)$

$u(x,t)=(x)q(t)=(A_{1}sin\frac{}{c}x+A_{2}cos\frac{}{c}x)(B_{1}sint+B_{2}cost)$

where $c=\sqrt[\phantom{2}]{\frac{E}{}}$