Chapter 4.4, Problem 20P

Assume that the system described by the equation $my\text{'}\text{'}+\gamma y\text{'}ky=0$ is critically damped and that the initial conditions are $y\left(0\right)=y_0,y\text{'}\left(0\right)=v_0$. If $v_0=0$, show that $y\to 0$ as $t\to \infty$ but that $y$ is never zero. If $y_0$ is positive, determine a condition on $v_0$ that will ensure that the mass passes through its equilibrium position after it is released.