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Homework Help: Laplace & Inverse Laplace Transforms

  1. Oct 19, 2008 #1
    1. The problem statement, all variables and given/known data
    L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
    L[f(t)]= ln(s+a) where 'a' is a constant

    2. Relevant equations

    3. The attempt at a solution
    I know that the inverse laplace of 1/(s^2+1) is sin(t), but how do I deal with the squared form of it.

    I have never encountered a logarithmic funcion for laplace, so can it be inverted back to f(t) with some of the common solution of conversion?

  2. jcsd
  3. Oct 20, 2008 #2


    Staff: Mentor

    For the first problem, and using a table of Laplace transforms, I see that:
    L(1/(2w^2)(sin (wt) - wt cos(wt)) = 1/(s^2 + w^2)^2
    and L(sin(wt)) = w/(s^2 + w^2)

    I'm stumped on the other problem
  4. Oct 20, 2008 #3


    User Avatar
    Science Advisor

    No elementary function has ln(s+a) as its Laplace transform.
  5. Oct 21, 2008 #4
    f(t) = (-t)^n[f(t)]
    F(s) = F(s)^nth derivative

    I believe that's what I got to do for the second one. thanks
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