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Homework Help: Laplace transform

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the laplace transform of;

    t*u(t-1)

    I always thought that the laplace transform of the function was;

    (1/s^2) * (e^-s)

    However, recently I was told that I was wrong!

    I was told that I was wrong, because t*u(t-1) is not a function of (t-1). That in order to take the proper laplace transform of it, I needed it to turn it into a function of (t-1).

    How can I do that? Can anyone help me find the proper laplace transform of my function, please?
     
  2. jcsd
  3. Dec 1, 2008 #2
    okay, this isn't too hard, let's start out with the definition of the laplace transform:

    [tex]\int_0^\infty t u(t-1) e^{-st} dt= \int_1^\infty t e^{-st} dt[/tex]

    and then you just need to evaluate the integral, which will give you something like:
    [tex]\frac{e^{-s}(s+1)}{s^2}[/tex]
     
  4. Dec 1, 2008 #3
    Thank you, I did everything and got the same result. :]
     
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