L^−1 {1 − e^−s/s(1 − e^−2s)} = ?

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- Dec 9th 2009, 04:36 AMessedraHow to solve this inverse Laplace transform?
L^−1 {1 − e^−s/s(1 − e^−2s)} = ?

- Dec 9th 2009, 04:43 AMCaptainBlack
- Dec 11th 2009, 05:32 AMessedra
- Dec 11th 2009, 06:28 AMJester
With CB's simplification re-write as

$\displaystyle

\mathcal{L}^{-1}\left[

\frac{1}{s(1+e^{-s})}

\right] =

\mathcal{L}^{-1}\left[

\frac{1}{s} - \frac{e^{-s}}{s} + \frac{e^{-2s}}{s} - \frac{e^{-3s}}{s} \pm \cdots

\right]

$

The inverse Laplace transform of each gives a series of step functions and together a square wave. - Jan 15th 2010, 07:51 AMmabel lizzy
- Jan 15th 2010, 02:55 PMmr fantastic