Answer
$v = \sqrt{\frac{kL(L-L_0)}{m}}$
Work Step by Step
We know that Force is given by $F= k(L-L_0)$. Using the fact that $\mu$ is a constant of mass per unit length, we can simplify the following equation for speed:
$ v = \sqrt{\frac{F}{\mu}}= \sqrt{\frac{k(L-L_0)}{\frac{m}{L}}}=\sqrt{\frac{kL(L-L_0)}{m}}$
