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Math Help - How to solve this inverse Laplace transform?

  1. #1
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    How to solve this inverse Laplace transform?

    L^−1 {1 − e^−s/s(1 − e^−2s)} = ?
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  2. #2
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    Quote Originally Posted by essedra View Post
    L^−1 {1 − e^−s/s(1 − e^−2s)} = ?
    Do you mean:

     <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1-e^{-s}}{s(1-e^{-2s})}<br />
\right]=<br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s(1+e^{-s})}<br />
\right]<br />
?


    If so please more brackets in future to make your meaning clear.


    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Do you mean:

     <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1-e^{-s}}{s(1-e^{-2s})}<br />
\right]=<br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s(1+e^{-s})}<br />
\right]<br />
?


    If so please more brackets in future to make your meaning clear.


    CB
    Yes, this was the expression that I've tried to write... How can I solve this..?
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  4. #4
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    Quote Originally Posted by essedra View Post
    Yes, this was the expression that I've tried to write... How can I solve this..?
    Quote Originally Posted by CaptainBlack View Post
    Do you mean:

     <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1-e^{-s}}{s(1-e^{-2s})}<br />
\right]=<br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s(1+e^{-s})}<br />
\right]<br />
?


    If so please more brackets in future to make your meaning clear.


    CB
    With CB's simplification re-write as

     <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s(1+e^{-s})}<br />
\right] = <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s} - \frac{e^{-s}}{s} + \frac{e^{-2s}}{s} - \frac{e^{-3s}}{s} \pm \cdots<br />
\right]<br />

    The inverse Laplace transform of each gives a series of step functions and together a square wave.
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  5. #5
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    Quote Originally Posted by Danny View Post
    With CB's simplification re-write as

     <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s(1+e^{-s})}<br />
\right] = <br />
\mathcal{L}^{-1}\left[ <br />
\frac{1}{s} - \frac{e^{-s}}{s} + \frac{e^{-2s}}{s} - \frac{e^{-3s}}{s} \pm \cdots<br />
\right]<br />

    The inverse Laplace transform of each gives a series of step functions and together a square wave.
    Can you show me the Laplace inverse of -e^-s/s
    Last edited by mr fantastic; January 15th 2010 at 02:47 PM. Reason: Fixed post
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  6. #6
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    Quote Originally Posted by mabel lizzy View Post
    Can you show me the Laplace inverse of -e^-s/s
    You're expected to know that LT^{-1}\left[ e^{-as} f(s) \right] = F(t - a) for t > a and zero otherwise, where F(t) = LT^{-1}[f(s)].
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