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Inverse Laplace Transform

  1. Apr 17, 2012 #1
    Hi, I recently posted another question about a Laplace transform and now have a question about taking the inverse Laplace transform. Again, my professor did not cover this topic as well as I could have hoped for, and so I am stuck on this problem as well. Again, I understand the idea of Laplace transforms (and their inverses) very well, however actually computing them seems to be another issue. Anyway, here is the problem.

    2502qz9.png

    I saw a definition in the book that seemed like it could be useful, however, when I tried to implement it, things seemed to get ugly. Here's the definition I found:

    [itex]\ell^{-1}[/itex] [itex]\left\{\stackrel{F(s)}{s}\right\}[/itex] = [itex]\int^{t}_{0}[/itex] f([itex]\tau[/itex]) d[itex]\tau[/itex]

    Please note that due to my typing incompetency, I cannot figure out how to make fractions with the forum tools. That should be F(s)/s in the inverse Laplace transform brackets above.

    Any help or step in the right direction would be appreciated. thanks
     
  2. jcsd
  3. Apr 17, 2012 #2
    Since you have that formula, you observe in your problem that F(s)=(1-exp(-s))/(1+exp(-s)), which can be inverted by a little manipulation (and table look up). Then F(s)/s is inverted by integrating f(tau).
     
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