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Laplace transform of step function

  1. Feb 12, 2009 #1
    this isnt homework, this is just general knowledge and i cant figure it out.. please help, thx

    Find the Laplace transform of the given function:

    f(t) = { 0 t<2, (t-2)^2 t>=2

    I tried working it out and this is where i get stuck

    f(t) = (t-2)^2 * u(t-2)

    I am not sure if I got the write function for f(t), but if I did, I am not sure how to go on with solving this.
    Any help is appreciated, Thank YOu
  2. jcsd
  3. Feb 12, 2009 #2
    Are you trying to put this into a form that you can look it up in a table? Your statement "I am not sure if I got the right function for f(t)" is confusing since it's already given.

    Seems to me that you can do this by direct substutition into the definition of the transform:

    F(s) = \int_0^\infty e^{-st} f(t) dt

    put in your f(t), starting your integral at t=2, make a t-2 change of vars, and integrate by parts a couple times.
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