Chapter 4.4, Problem 11P

(a) A spring is stretched $10$ cm by a force of $3$ newtons $\left(N\right)$. A mass of $2$ kg is hung from the spring and is also attached to a viscous damper that exerts a force of $3$ N when the velocity of the mass is $5\text{m/s}$. If the mass pulled down $5$ cm below its equilibrium position and given an initial downward velocity of $10$ cm/s, determine its position $y$ at any time $t$. Find the quasi-frequency $v$ and the ratio of $v$ to the natural frequency of the corresponding undamped motion.

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