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Homework Help: Inverse Laplace transform

  1. Jul 14, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the inverse laplace transform of (s+1)/ (s^2 + 4s + 5) + e^-2s / 3s^4

    2. Relevant equations

    3. The attempt at a solution

    For the first one

    (s+1) / (s^2 + 4s + 5), I completed the square for the denominator so

    (s+1) / [(s+1)^2 + 1]

    Now it gets confusing, how do I find out the inverse laplace of this.

    And for e^-2s / 3s^4 , is the inverse laplace 1/9 x 1/ (s+2)^4 = 1/9(s+2)^4
  2. jcsd
  3. Jul 14, 2008 #2


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    Science Advisor

    The same way you find the inverse Laplace transform of just about anything: look it up in a table.
    If you don't have one in your book, here's one:

    You will notice that they give an inverse Laplace transform for [itex]s/(s^2+ \alpha[/itex] as well as the inverse Laplace transform for [itex]F(x-\alpha)[/itex]. Use them together for [itex] (s+1)/((s+1)^2+ 2)[/itex].
  4. Jul 14, 2008 #3
    The problem is I dont get the LaTeX Code: s/(s^2+ \\alpha thing. I only get the f(x +a) thing.
  5. Jul 14, 2008 #4
    In the last line of Ivy you should recognize a form that can be found in the table. Ivy rewrote the equation in that form by taking out a square.
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