Chapter 3.2, Problem 20E

For the harmonic oscillator with mass $m=1,$ spring constant $k=4,$ and damping coefficient $b=5$
(a) compute the eigenvalues and associated eigenvectors;
(b) for each eigenvalue, pick an associated eigenvector $V$ and determine the solution $Y(t)$ with $Y(0)=V$
(c) for each solution derived in part (b), plot its solution curve in the y v-phase plane;
(d) for each solution derived in part (b), plot its $y(t)$ - and $v(t)$ -graphs; and
(e) for each solution derived in part (b), give a brief description of the behavior of the mass-spring system.