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Homework Help: Diff Eq problem, Laplace Transform

  1. Jun 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the Laplace Transform of the given function

    I'm not sure how to add (t-1) to the t^2 term to solve the problem

    Any help would be greatly appreciated.
  2. jcsd
  3. Jun 20, 2009 #2
    That notation makes no sense, are you trying to translate the function on the s-axis? If you are what is the original function.
  4. Jun 20, 2009 #3
    If the original function is e^t*t^2 the translation = F(s-1) and since f(t)=t^2 its transform is 2/s^3, therefore you substitute s-1 in for s and get 2/(s-1)^3. Unless you are doing an inverse translation on the t-axis.
  5. Jun 21, 2009 #4
    My book states that it is a H(t) is a heavyside function and I'm suppose to use the proposition:

  6. Jul 14, 2009 #5
    Oh a unit step therefore you must translate both H(t) and F(t). LH(t-1)=e^s and f(t)=t^2, L(t^2)=2/s^3, so the transform is 2e^s/s^3
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