1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vibrating string displacement, partial differential problem

  1. Feb 9, 2008 #1
    1. The problem statement, all variables and given/known data
    A damped vibrating string of length 1, that satisfies
    u_tt = u_xx - ([tex]\beta[/tex])u_t

    with the boundary conditions:

    initial conditions:


    solve for u(x,t) if [tex]\beta[/tex]^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:


    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!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted