# vibrating string displacement, partial differential problem

by leoflc
Tags: differential, displacement, partial, string, vibrating
 P: 56 1. The problem statement, all variables and given/known data A damped vibrating string of length 1, that satisfies u_tt = u_xx - ($$\beta$$)u_t with the boundary conditions: u(0,t)=0 u(1,t)=0 initial conditions: u(x,0)=f(x) u_t(x,t)=0 solve for u(x,t) if $$\beta$$^2 < 4Pi^2 3. The attempt at a solution if u(x,t)=F(x)G(t) So by using partial differential equations, I got: G''+$$\beta$$G'+GP^2=0 and F''+FP^2=0 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 $$\beta$$ to solve for u(x,t). Thank you very much!

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