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Homework Help: Inverse Laplace Help

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the inverse laplace transform of the equation listed:


    2. Relevant equations

    a, R, C, and L are constants.

    3. The attempt at a solution

    Completely lost, not sure how to even begin to reduce this massive function.
  2. jcsd
  3. Oct 9, 2011 #2
  4. Oct 9, 2011 #3
    If I complete the square term on the bottom (s^2 + s + c) => (s + x)^2 + c, where does the additional x^2 term go that I added? Does it get added to the numerator also? It's been a while since I've done this stuff before.
  5. Oct 9, 2011 #4
    So you want to transform:


    I'd have to review that also but as far as completing the square, you'd write:


    or to make it a little easier, just let f=c-1/4 so that we need to invert now:


    Yeah, well I don't know how to do that one either. I'd have to review. I did it in Mathematica and it looks pretty messy but the more you work on these, the easier they get.
  6. Oct 9, 2011 #5
    Well, after completing the square and then subtracting out what I added to complete the square, I get this (It's a bit messy):

  7. Oct 9, 2011 #6
    Ok, that's a good start although you're quick to jump right back to the complicated problem. So Let me work a simple one that's related using the exponential shifting theorem:

    Suppose I have:


    I now write that as:


    Now we can use the shifting theorem:


    where F(t) is the inverse transform of f(s).

    You can figure that out.
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