Prove that x(t) = C1cos(wt)+c2sin(wt)+(F0/2mw))tsinwt

w = omega

Consider a spring with mass m, spring constant k, and damping constant c = 0, and let w = root(k/m). If an external force F(t) = F0cos(wt) is applied(the applied frequency = the natural frequency), use the method of undetermined coefficients to show that that the motion of the mass is given by x(t) (above).

I got it to mr^2 + kx = F0cos(wt)

I found the root and came out to +_ wi and i was able to get the first part of x(t). Xc(t) = C1 cos(wt) + c2sin(wt)

can someone help me get the 2nd part?

I tried Xp(t) = ACos(wt)+BSin(wt) and i tried At(coswt)+BtSin(wt) and i couldn't get it down to that.

any help?? Thanks