An un-damped driven harmonic oscillator satisfies the equation of motion: ma+kx=F(t) where we may write the un-damped angular frequency w-naught^2=k/m. The driving force F(t)=F-naught*sin(wt) is switched on at t=0. Find x(t) for t>0 for initial conditions x=0, v=0,at t=0.
I know that this can be written in terms of a complimentary and a particular solution and that the complimentary solution will be in the form x(t)=Asin(w-naught*t-delta) and that I need to consider a particular solution in the form x(t)=Asin(wt) and determine A by plugging x(t) into the differential equation.
The Attempt at a Solution
The final answer is given as x(t)= -((F-naught/m)(w/w-naught)/(w-naught^2-w^2)) sin(w-naught*t) + ((F-naught/m)/(w-naught^2-w^2)) sin(wt)
Ive done similar problems that have worked out but for some reason I can't get this to come out right. It's driving me nuts I've been working on it all weekend and have to turn this work in tomorrow morning.