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Math Help - need help with separation or variable to solve wave equation

  1. #1
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    need help with separation or variable to solve wave equation

    i have to use method of separation of variable to solve the wave equation below. I have no idea where to start the calculation. please help~!!
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  2. #2
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    If you are given, \frac{\partial^2 u}{\partial t^2} = k^2 \frac{\partial^2 u}{\partial x^2} ( k>0)
    With boundary conditions u(0,t) = u(\pi,t) = 0.
    And with initial conditions u(x,0) = f(x) and u_t(x,0) = g(x).
    Where f(x) = \sum_{n=1}^N b_n \sin (nx) and g(x) = \sum_{n=1}^N a_n \sin (nx).
    The solution is given by,
    u(x,t) = \sum_{n=1}^N \left[ \frac{a_n}{kn} \sin (nt) + b_n \cos (nt) \right] \sin (nx)
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