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Inverse Laplace?

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Any way to reduce this function for simplification? (Trying to find the reverse Laplace function) I found this function after doing a circuit analysis on a transmission line.

    [tex] \frac{s^2RC+sL}{s^2RC+sL+R} [/tex]

    2. Relevant equations

    none


    3. The attempt at a solution

    I couldn't arrive at anything past this
     
  2. jcsd
  3. Oct 6, 2011 #2

    HallsofIvy

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    Staff Emeritus
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    Well, seeing "[itex]s^2RC+ sL[/itex]" in both numerator and denominator, the first thing I would do is divide [itex]s^2RC+ sL+ R[/itex] into [itex]s^2RC+ sL[/itex]. Obviously, it will go into it once with remainder [itex](s^2RC+ sL)- (s^2RC+ sL+ R)= -R[/itex].

    That is
    [tex]\frac{s^2RC+ sL}{s^2RC+ sL+ R}= 1-\frac{R}{s^2RC+ sL+ R}[/tex]

    Now, if s is the variable, complete the square in the denominator.
     
  4. Oct 6, 2011 #3
    holy cow that was quick. Many thanks. I think that works out.
     
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