A particle of mass m undergoes one-dimensional damped harmonic oscillations with a damping constant gamma and a natural frequency omega nought. In addition the particle is subject to a time dependent external force given by: Fext = f1t + f2t^2 a) What is the differential equation that governs the motion of the particle? I found Xp(t) but I don't know what the homogeneous solution is because it doesn't specify if it's underdamped, overdamped, or critcally damped. How do I know? b) Determine what the "steady-state" solution will be at late times after all the transient motions have damped out. So the particular solution will disappear because at t approaches infinity those terms with t will vanish. But I can't complete the question if I don't know the homogenous solution.