Chapter 4.4, Problem 24P

The position of a certain spring-mass system satisfies the initial value problem

$\begin{array}{ccc}\frac{3}{2}y\text{'}\text{'}+ky=0,& y\left(0\right)=2,& y\text{'}\left(0\right)=v\end{array}$.

If the period and amplitude of the resulting motion are observed to be $\pi$ and $3$, respectively, determine the values of $k$ and $v$.