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Piece wise function and Laplace Transform

  1. Apr 1, 2006 #1
    Hi,
    I need to find the piece wise function whose the the Laplace Transform is:

    2/s+e-3x(1/s2)+4e-3x(1/s)

    I found for f as function of the unit step function u:
    f(x)=2+x*u(x-3)+u(x-3)

    Now I have difficulty to put the function in piece wise form like:

    f(x)= 2 for 0<x<2 and f(x)=........ for x>3

    How can I found the expression of f(x) for x>3??

    Thank you
    B
     
  2. jcsd
  3. Apr 2, 2006 #2
    The definition of the heaviside unit step function is:

    [tex] U(t-t_0) = \left[ \begin{array}{c}1\,\,t\geq t_0 \\ 0\,\,t<t_0 \end{array} [/tex]

    right?

    so:

    first factor your function:
    [tex] f(x)=2+x*u(x-3)+u(x-3) [/tex]

    [tex] f(x) = 2+u(x-3)(x+1) [/tex]
    Now plug in the definition of the function:


    [tex] f(x)=2+(1)(x+1) \,\,\,t \geq 3 [/tex]
    [tex] f(x)=2+(0)(x+1) \,\,\,t < 3 [/tex]

    does that makes sense?
     
    Last edited: Apr 2, 2006
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