you're saying I should express the solution, which is x=A sin (omega*t - phi) in terms of sin and cos. I would need to start with a solution in the form of sin u + sin (u + pi/2), which is not what you start with, so I don't think that's possible.
Also, by the way, I am pretty sure that the...
Even if phi is not a constant, but dependent on omega? it seems like that would make it even more complicated...how would I do this?
do you mean something like sin u + cos u = sin u + sin (u + pi/2)? how would that help?
But how can I assume a solution; the solution is given to me and there is only sin, there is no cos term in it. The magnitude for A that you have given is only true is certain cases I think, such as when there is no external force.
A should be dependent on omega, not on the constants A and B.
Edit: Trying to be more clear: This is what I tried.
I first plug the steady state solution into the differential equation for the damped harmonic oscillator, with an external force = F sin (omega*t).
I end up with an equation that has imaginary numbers only on the LEFT side of the equation...
Homework Statement
A damped harmonic oscillator is driven by a force
F external= F sin (omega * t)
where F is a constant, and t is time.
Show that the steady state solution is given by
x(t)= A sin (omega * t - phi)
where A is really A of (omega), the expression for the amplitude...
ok, I have searched for this topic and found a couple of responses, but no conclusive answer so I thought Id ask...if I am at a school that only offers a BA, will I be at a disadvantage getting a BA in physics or should I transfer to another city university that offers the BS with very similar...