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 yv-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.
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