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Homework Help: Inverse Laplace transformation

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data

    I'm supposed to find the inverse Laplace transformation of the following equation

    2. Relevant equations

    G(s) = s+1/s2+25

    3. The attempt at a solution

    I was thinking of using one of the shifting theorems because I know that L-1 {1/s2+25} is just sin(5t) but I don't know how to get rid of the numerator.
     
  2. jcsd
  3. Mar 29, 2010 #2

    Mark44

    Staff: Mentor

    You should get into the habit of using parentheses to write rational expressions correctly.

    This is how what you wrote would be interpreted:
    [tex]G(s) = s + \frac{1}{s^2} + 25[/tex]

    Here is what I believe you really meant:
    [tex]G(s) = \frac{s + 1}{s^2 + 25}[/tex]

    To convey what I think you meant when you write in on one line, use parentheses.
    G(s) = (s + 1)/(s2 + 25)

    Split your expression to get G(s) = s/(s2 + 25) + 1/(s2 + 25). From that you can get L-1(G(s)) = L-1( s/(s2 + 25)) + L-1(1/(s2 + 25)), both of which are straightforward.
     
    Last edited: Mar 29, 2010
  4. Mar 29, 2010 #3
    Yes that is what I meant to type, my mistake.

    I didn't even think of separating the numerator of the equation. :blushing: But I see exactly what you mean.

    Thank you so much for the help and the quick reply!
     
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