(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A damped harmonic oscillator is displaced a distance xo from equilibrium and released with zero initial velocity. Find the motion in the underdamped, critically damped, and overdamped case.

2. Relevant equations

d^{2}x/dt^{2}+ 2K dx/dt + ω^{2}x = 0

Underdamped: x = C*e^{-Kt}cos(ωt-[itex]\gamma[/itex])

Overdamped: x = A*e^{-K-t}+B*e^{-K+t}

Critically Damped: a*e^{-Kt}*(1+bKt)

3. The attempt at a solution

I haven't attempted the solution because I'm not sure how to incorporate xo into the equations. I understand that at time t=0, x=xo, but how do I use this fact? Any help would be greatly appreciated. Thank you in advance.

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# Homework Help: Damped Harmonic Oscillator - Help Please

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