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Laplace Transform

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Is it possible to do the inverse laplace transform for this?

    F(s) = [tex]\Sigma[/tex][e^(ns)]/s where n=0 and goes to infinity


    2. Relevant equations
    u_c(t) = [e^-(cs)]/s

    3. The attempt at a solution

    I don't think I can use this conversion because c or s is never less than 0... So is there another method to approach this problem?

    Thank you in advance.
     
  2. jcsd
  3. Oct 23, 2008 #2
    Well I think, the sum converges,

    [tex]\sum_{n=0}^{\infty}\frac{e^{ns}}{s}=\frac{-1}{(e^s-1)s}[/tex]

    So it will just be

    [tex]-\mathcal{L}^{-1} \left\{ \frac{1}{(e^s-1)s} \right\} [/tex]
     
  4. Oct 23, 2008 #3
    Oh, so there's no way to express it in terms of t? or even express [e^ns]/s in terms of t?
     
  5. Oct 23, 2008 #4
    Well when you take the inverse laplace transform, in that last equation I wrote you will get it in terms of t. I was just showing you that the sum converges so you can simplify it.

    [tex]f(t)=-\mathcal{L}^{-1} \left\{ \frac{1}{(e^s-1)s} \right\}[/tex]
     
  6. Oct 23, 2008 #5
    Okay, I understand that. But I don't see any elementary laplace transform which has F(s) = e^s ... All of them has a negative sign in front of the s: e^-s. So i couldn't possibly set e^s/s = u_c(t)
     
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