Driven, damped harmonic oscillator -- need help with particular solution Consider a damped oscillator with Beta = w/4 driven by F=A1cos(wt)+A2cos(3wt). Find x(t). I know that x(t) is the solution to the system with the above drive force. I know that if an external driving force applied to the oscillator then the total force is described by F = -kx - bx' + F0cos(wt). But in our case the driving force is A1cos(wt)+A2cos(3wt) so F=-kx-bx+A1cos(wt)+A2cos(3wt). Then our differential equation is mx''+bx'+kx=A1cos(wt)+A2cos(3wt). This can also be written as x''+2Betax'+(w^2)x=A1cos(wt)+A2cos(3wt). For the complementary solution, we set the right side of the equation equal to zero and solve for x. This is o.k. However, I am having trouble with the particular solution. Can someone tell me how I find a particular solution for this? I can find the particular solution for x''+2Beta x'+ (w^2)x = A cos (wt), but what about the particular solution when the driving force is not A cos (wt), as we have in this case? Any help GREATLY appreciated!