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I am styding Laplace transforms and for some reason I have stuck in the followning exercise.

Find the inverse Laplace Transform $ L^{-1} \{\log \frac{s^2 - a^2}{s^2} \}$.

Any help?

Thank's in advance!

1 Answers 1

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If

$F(s)=\mathcal{L}\{f(t)\}(s)=\log(1-s^2/a^2)$

then

$\mathcal{L}\{t f(t)\}=-F'(s)=-\frac{d}{ds}\log(1-a^2/s^2)=\frac{2}{s}-\frac{1}{s+a}-\frac{1}{s-a}.$

Now, can you apply the inverse Laplace transform to both sides here? Then just divide by $t$.

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    @pbs Right, thanks.2013-01-25