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Laplace transform of |sint|

  1. Apr 2, 2010 #1
    1. The problem statement, all variables and given/known data Need to find the Laplace transform of |sint| (modulus).



    2. Relevant equations



    3. The attempt at a solution I am really not sure how to proceed here - any help would be much appreciated.
     
  2. jcsd
  3. Apr 2, 2010 #2

    Mark44

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    |sin(t)| = sin(t) on [0, pi], and |sin(t)| = -sin(t) on [pi, 2pi] or on [-pi, 0]
     
  4. Apr 2, 2010 #3

    vela

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    I don't know if this is the best way to go about it, but perhaps you can express the function as a convolution of a half wave with a train of delta functions (or something like that).
     
  5. Apr 2, 2010 #4
    Thanks - I thought of this as well, but this would mean I have to integrate on each interval, and I get sum(n=0, n=inf) ((1+exp(pi*s)/exp(n*pi*s)*(s^2+1)). Is there a way to simplify this? I'm supposed to be using Laplace transforms to solve a differential equation with |sint| as the inhomogeneous part.
     
  6. Apr 2, 2010 #5

    vela

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    Think geometric series where r=exp(-pi*s).
     
  7. Apr 2, 2010 #6
    Ah of course, thanks :)
     
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