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 d2x/dt2 + 2K dx/dt + ω2x = 0 Underdamped: x = C*e-Ktcos(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.