Help me do some algebra!

[Matt R.]

OK, so I'm trying to find the angular frequency of a particle underdoing simple harmonic motion. It has a velocity x1' when the displacement is x1 and a velocity x2' when the displacement is x2.

I'm not 100% sure the method that I used to get this equality is correct (but I think it is). Basically, I'm more concerned with the algebra at this point and whether or not it is solvable.... If it's not solvable I know I need to go a different route.

So, I need to solve for angular frequency, w, in terms of x1 x1' x2 and x2'. Here is the equality:

x1 cos (wt) + (x1'/w)sin wt = -(x2'/w)cos wt + x2 sin wt

Again, I need to solve this equation for w in terms of the displacements and velocities. I cannot properly get rid of the sine and cosine terms. I'm always "off" by a minus sign somewhere. I thought I solved it once, and it was close, but the signs were slightly off from the correct answer.

Any help would be appreciated!