# Inverse Laplace transform

• Mar 16th 2008, 10:47 AM
al2308
Inverse Laplace transform
I've got to find the inverse laplace transform of the following

L-1 [(e^-sTd)/((1+sTp)s)]

where Td=0.165 Tp=0.63

I'm not sure how to go about this one as it contains the eponential on the top. I'm sure there must be some way to get rid of it before carrying out the inverse transform. But i'm not sure how.
• Mar 16th 2008, 10:56 AM
Jhevon
Quote:

Originally Posted by al2308
I've got to find the inverse laplace transform of the following

L-1 [(e^-sTd)/((1+sTp)s)]

where Td=0.165 Tp=0.63

I'm not sure how to go about this one as it contains the eponential on the top. I'm sure there must be some way to get rid of it before carrying out the inverse transform. But i'm not sure how.

here is a general formula that may be of assistance:

$\mathcal{L}^{-1} \left( e^{-cs} F(s) \right) = u_c(t)f(t - c)$

where $f(t) = \mathcal{L}^{-1} F(s)$

and $u_c(t) = \left \{ \begin{array}{lrr} 0, & \mbox{ if } t < c & \\ & & c \ge 0 \\ 1, & \mbox{ if } t \ge c & \end{array} \right.$