Chapter 4.4, Problem 9P

(a) A mass of $20$ g stretches a spring $5$ cm. Suppose that the mass is also attached to a viscous damper with a damping constant of $400\text{dyne}\cdot \text{s/cm}$. If the mass is pulled down an additional $2\text{cm}$ and then released, find its position $y$ at any time $t$. Plot $y$ versus $t$. Determine the quasi-frequency and the quasi-period. Determine the ratio of the quasi-period to the period of the corresponding undamped motion. Also find the time $\tau$ such that $\left|y\left(t\right)\right|<0.05\text{cm}$ for all $t>\tau$.

(b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the initial value problem in part (a).