Chapter 4.4, Problem 10P

A mass weighing $16$ lb stretches a spring $3\text{in}$. The mass is attached to a viscous damper with a damping constant of $2\text{lb}\cdot \text{s/ft}$. If the mass is set in motion from its equilibrium position with a downward velocity of $3\text{in}\text{./s}$, find its position $y$ at any time $t$. Plot $y$ versus $t$. Determine when the mass first returns to its equilibrium position. Also find the time $\tau$ such that $\left|y\left(t\right)\right|<0.01$ in for all $t>\tau$.