Nonhomogeneous: Undetermined coefficients

(d^2x/dt^2)+(w^2)x=Fsin(wt), x(0)=0,x'(0)=0

Hope that's readable. First part is second derivative of x with respect to t. w is a constant and F is a constant. I need to find a solution to this using method of undetermined coeffecients and I'm confused with all the different variables. Anyone get me started at least?

Pyrrhus
Homework Helper
Well, first off start by solving the homogenous equation to find the fundamental solution.

$$\ddot{x} + \omega^{2}x = 0$$

After that try a Particular solution of the type

$$y_{p} = A x \sin(\omega t) + B x\cos(\omega t)$$

Remember that if the fundamental solution has already sin and cos, you will need to try a xsin and xcos, like this case.

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I got my homogenous equation x''+(w^2)x=0 but I can't find my roots with that w^2 in there.

Pyrrhus
Homework Helper
What seems to be the problem? Show me your work.

Pyrrhus
Homework Helper
Here, i will start you off

$$\ddot{x} + \omega^{2}x = 0$$

we assume a as a solution

$$x(t) = e^{rt}$$

So we substitute in our ODE

$$r^{2}e^{rt} + \omega^{2}e^{rt} = 0$$

so

$$e^{rt}(r^{2} + \omega^{2}) = 0$$

because $e^{rt}$ cannot be equal to 0

$$r^{2} + \omega^{2} = 0$$

which ends up as

$$r = \pm \omega i$$

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I figured it out, thanks a lot for your help, I was just being dumb.