# Un-damped Driven Harmonic Oscillator Question

## Homework Statement

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.

## Homework Equations

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.

## The Attempt at a Solution

gabbagabbahey
Homework Helper
Gold Member
What do you get for A when you plug your particular solution into the DE....what does that give you for your general solution?

ok, i got that part. A will equal (F-naught/m)/(w-naught^2-w^2). I think I was just writing it wrong when I plugged into the DE. Now I just have to work through the complimentary part.

hmm, I know this should be the easy part but I'm stuck again! I can't seem to figure out how to solve for A in the complimentary part.

gabbagabbahey
Homework Helper
Gold Member
You'll have to use the initial condition that you were given: x(0)=x'(0)=0....remember that these condition apply to the total solution, not just the complimentary part.

thanks, thats whats probably getting me here. appreciate all the help