1. The problem statement, all variables and given/known data "The equation mx'' + kx = F0 * Sin (wt) governs the motion of an undamped harmonic oscillator driven by a sinusoidal force of angular frequency w. Show that the steady-state solution is x = F0 * Sin (wt) /(m * (w0^2 - w^2)) 2. Relevant equations x(t) = xta(t) + xtr(t) where xta = long term behavior and xtr = transient piece of solution xta(t) x0 cos (wt - (phi) where x0 = w0^2 X0/[(w0^2 - w^2)^2 + v^2*w^2]^1/2 and phi = tan^-1(vw/(w0^2 - w^2) 3. The attempt at a solution Honestly I'm not sure if the above equations are necessary. All my lecture notes tell me is that the long term behavior follows x0 * cos(wt - (phi)) so I'm not sure how I'm suppose to take that and turn it into F0 * Sin (wt) /(m * (w0^2 - w^2)) I mean obviously I have a sin force driving my harmonic oscillator, but how do I use that to determine my long term solution? I really can't go much further than this at this point, I've been looking at this problem for a long time now and I can't scrap together anything useful.