1. The problem statement, all variables and given/known data Solve for the steady-statem otion of a forced oscillator if the forcing is F_0*sin(wt) instead of F_0*cos(wt). Use complex representations. 2. Relevant equations e^(i*x) = cos(x)+isin(x) 3. The attempt at a solution I assume, First, steady-state means without damping. Next, we have the equation m*x'' = -kx + F_0*sin(wt) where x'' is the second derivative of x position with respect to time. Also known as acceleration. So, we have: z'' + w_0^2*z = F_0/m * (-i*e^(iwt)) where Re(z) = x So far so good? I think I changed it correctly, normally when you do F_0*cos(wt) as forcing, you just switch it to e^(iwt) Now, if everything is looking good up to here, we take z = A*(-ie^[i(wt-φ)]) After taking the second derivative of this and inputting it into our equation, our equation looks like: i*w^2*A*e^[i(wt-φ)]-w_0^2*A*i*e^[i(wt-φ)] = F_0/m * (-i*e^(iwt)) dividing through by -i*e^(iwt) nets us F_0/m = A(w_0^2 - w^2)*e^(-iφ) Simplifying: F_0/m *e^(iφ) = A(w_0^2-w^2) But now I seem to have run into a problem. The real part of this is F_0/m*cos(φ) But this is the exact same solution to the forcing with F_0*cos(wt). I thought the problem wants me to reach Re(z) = F_0*sin(wt) Any help? Did I go wrong somewhere?