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Homework Help: Laplace Transform Problems

  1. Nov 7, 2008 #1
    1. The problem statement, all variables and given/known data
    find the laplace transform of g(t) = t u(t-2) using the basic definition.


    2. Relevant equations
    L{f(t)} = ∫f(t)e-stdt from 0 to infinity

    3. The attempt at a solution
    I am able to get the transform by applying the t-shifting property. However, how do I do it by using basic definition? thanks.
     
  2. jcsd
  3. Nov 7, 2008 #2

    HallsofIvy

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    Science Advisor

    By integrating! Since H(x) is defined to be 0 for x< 0, 1 for x>= 0, H(t-2)= 0 for t< 2, 1 for t<= 2.
    [tex]L{f(t)}= \int_2^\infty t e^{-st}dt[/tex]
    That should be easy.
     
  4. Nov 7, 2008 #3
    Thank you very much. One more question. what is the inverse laplace transform of 1? Is it possible to get it? if there is, what can be done? thanks..
     
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