Un-damped Driven Harmonic Oscillator Question

  • #1

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
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What do you get for A when you plug your particular solution into the DE....what does that give you for your general solution?
 
  • #3
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.
 
  • #4
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.
 
  • #5
gabbagabbahey
Homework Helper
Gold Member
5,002
7
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.
 
  • #6
thanks, thats whats probably getting me here. appreciate all the help
 

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