Question: Consider the harmonic oscillator system a) For which values of k, b does this system have complex eigenvalues? repeated eigenvalues? Real and distinct eigenvalues? b)

Consider the harmonic oscillator system

a) For which values of k, b does this system have complex eigenvalues? repeated eigenvalues? Real and distinct eigenvalues?

b) Find the general solution of this system in each case.

c) Describe the motion of the mass when is released from the initial position x=1 with zero velocity in each of the cases in part (a).

X' = 0 1 -k-b,

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