(Solved): 5) A harmonic oscillator can be described as underdamped, overdamped, or critically damped by look ...

5) A harmonic oscillator can be described as underdamped, overdamped, or critically damped by looking at is eigenvalue. ? b) ? If the eigenvalue is complex the oscillator is underdamped and the equilibrium solution will be a spiral sink. If the eigenvalue has two distinct real solutions the oscillator is overdamped and the equilibrium solution will be a sink. If there is only one eigenvalue the oscillator is critically damped. (This never happens in reality. Graph the phase plane of one of these and you'll see why.) Given the above information determine whether each harmonic oscillator is overdamped, underdamped, or critically damped. Your answer should include the eigenvalues of each system. a) x" + 1x' + 7x = 0 x" +5x+x=0 x" +16x' + 64x = 0