# Inverse Laplace Transform

• Jun 14th 2009, 11:56 PM
simplependulum
Inverse Laplace Transform
Find the inverse laplace transform :

$\displaystyle F(s) = \sqrt{ s + \sqrt{1+s^2}}$
• Jun 16th 2009, 05:49 AM
The Second Solution
Quote:

Originally Posted by simplependulum
Find the inverse laplace transform :

$\displaystyle F(s) = \sqrt{ s + \sqrt{1+s^2}}$

Has this arisen from a problem you're working on or have you been asked point blank to find it?
• Jun 16th 2009, 10:50 AM
shawsend
Quote:

Originally Posted by simplependulum
Find the inverse laplace transform :

$\displaystyle F(s) = \sqrt{ s + \sqrt{1+s^2}}$

If you mean Bromwich style, then look at this one first:

$\displaystyle \mathop\oint\limits_{H} e^{st}\sqrt{1+s^2}\,ds$ where $\displaystyle H$ is the contour below. It doesn't matter if this one doesn't have an inverse transform. Just first figure out how the integrand varies across the (finite) red-blue and yellow-green branch-cuts and also the remaining parts of the contour. Then try and extend that work to $\displaystyle F(s)$ above. However, this may not be the best contour to use.