A damped vibrating string of length 1, that satisfies
u_tt = u_xx - ([tex]\beta[/tex])u_t
with the boundary conditions:
solve for u(x,t) if [tex]\beta[/tex]^2 < 4Pi^2
The Attempt at a Solution
So by using partial differential equations, I got:
I solved for F(x) with B.Cs and got:
F(x)=C*Sin(P*x), where C is a const.
when I tried to solve for G(t), I got a long equation with 2 constants in there.
If I try to solve for u(x,t) by using the F(x)G(t), I will have something with three unknow constants.
Am I on the right track?
I'm not sure how/when to apply I.Cs and [tex]\beta[/tex] to solve for u(x,t).
Thank you very much!