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Laplace Transform - Step Functions

  1. Jun 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Please help by explaining in detail how to find the Laplace transform of the function

    f(t) = { 2 0 <= t < 3
    { -2 t >= 3.





    2. Relevant equations



    3. The attempt at a solution
    For the most part I know that U(t-3)(t-3).

    I want to account for the amplitude of 2 like this but I think that I am wrong.

    2-2U(t-3)*-2(t-3). I feel that I'm on the right track but might have set up the problem incorrectly. if I have it set up correctly I think I can go from there but would like directional help please.

    Thank You,

    Lady Ann.
     
  2. jcsd
  3. Jun 24, 2008 #2

    Defennder

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    Homework Helper

    No I don't think that is correct.

    In general, if

    [tex]f(t)= g(t) \ \mbox{for} \ a\leq t \leq b[/tex] and is zero everywhere else, then

    [tex]f(t) = g(t)[u(t-a) - u(t-b)][/tex].
     
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