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Homework Help: Laplace Transform Time Shift problem

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the Laplace transform:

    g(t) = 2*e[itex]^{-4t}[/itex]u(t-1)

    3. The attempt at a solution

    Essentially we're told for a time shift we multiply the Laplace transform pair of the function (without the delay) by e[itex]^{-as}[/itex]

    So here a = 1 (for the delay)

    The Laplace transform for e[itex]^{-4t}[/itex] is [itex]\frac{1}{s + 4}[/itex]

    Multiplying we should get e[itex]^{-s}[/itex]([itex]\frac{2}{s + 4}[/itex])

    However the answer is e[itex]^{-s}[/itex]*([itex]\frac{2}{s + 4}[/itex]) * [itex]\frac{1}{e^{4}}[/itex]
    Last edited: Apr 3, 2012
  2. jcsd
  3. Apr 4, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Shifting is tricky.

    You have used the formula L{f(t-a)U(t-a)} = e-asL{f(t)}.

    You need the formula for L{f(t)U(t-a)}.
  4. Apr 4, 2012 #3
    It's because you must be in the form
    Take a look at your exponential. It isn't time-shifted by a to the right. What you can do is use the fact that exponentials multiplied add their exponents and the fact that e^b/e^b = 1, so you can multiply by it without changing your values. So you choose e^b so that you can add its exponents and arrive to the needed shift. The e^b in the denominator is factored outside of the linear inverse Laplace operator and you go from there.
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