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Homework Help: 1D wave PDE with extended periodic IC

  1. Oct 6, 2005 #1
    I have formula for 1D wave equation:

    (*) u(x, t) = 1/2 [ f(x + ct) + f(x - ct) ] + 1 / (2c) Integral( g(s), wrt
    s, from x-ct to x+ct )

    I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1 -
    x).

    However, for (*) to work, the initial position f(x) and initial velocity
    g(x) must be extended to periodic functions.

    "To determine f(x) and g(x) we need only find the integer n s.t. nL <= x <
    (n+1)L, [where L is the right boundary length from the origin]."

    It then gives the ways of extending if n is even or odd. If even, gx) =
    g(x - nL). If odd, g(x) = -g((n+1)L - x).

    How do I determine what n is for g to extend it correctly?

    I need to figure out nL <= x < (n+1)L, yes. But what is x for g? For
    f(x+ct) it is clear. But g is in the integral...
     
  2. jcsd
  3. Oct 6, 2005 #2
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