1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Method of separation of variables for wave equation

  1. Apr 25, 2013 #1
    1. The problem statement, all variables and given/known data
    $$u_{tt} = a^2u_{xx} , 0<x< l , t>0 , $$a is constant
    $$ u(x,0)=sinx , u_{t} (x,0) = cosx , 0<x< l , t>0 $$
    $$ u(0,t)=2t , u(l,t)=t^2 , t>0 $$

    2. Relevant equations

    3. The attempt at a solution
    I can solve the eigenvalue problem of X(x), and then solve for T(t), but I dont know how to solve the initial value problem for $$u(x,0) =sinx , and u_{t} (x,0) = cosx $$
    with I can only compute the fourier expansion of $$ sinx $$ and $$ cosx $$ with $$ λ_{n} = \frac { (n \pi)^2} {l^2} $$ , but the ans looks like ugly, and compare term is fail.
    by the way I'm sorry for my poor english.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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