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Finding the inverse laplace transform of (2/(s+2)^4) using Convolution theorem.

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities:

    2. Relevant equations
    Here are the given identities:
    FWlY5.png

    3. The attempt at a solution
    Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this identity is not on our formula sheet, so I decided to try it with convolution theorem.

    xiuk2.jpg

    What did I do wrong and also is there an easier way given the table of identities? Thanks!
     
  2. jcsd
  3. Dec 2, 2012 #2

    lurflurf

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    Homework Helper

    Where did you get that flawed table? Discard it.

    [tex]G(s)H(s) \rightarrow \int_0^t g(t-\tau)h(\tau) \mathop{d\tau}[/tex]

    Clearly both functions should depend on the integration variable.
     
    Last edited: Dec 2, 2012
  4. Dec 2, 2012 #3
    Ahh, thanks!

    This is the table that we get for our midterms and final lol :yuck:

    Is there an easier way to solve this with another identity? The integral is pretty messy.
     
  5. Dec 2, 2012 #4

    lurflurf

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    Homework Helper

    That integral is not so bad, and you wanted to avoid using

    [tex]\frac{1}{(s+a)^{n+1}} \rightarrow \frac{t^n}{n!} e^{-a \mathop{t}}[/tex]

    you could derive it. It helps to have a longer table with fewer errors.
     
    Last edited: Dec 2, 2012
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