Inverse Laplace transform

**al2308** · March 16th 2008, 10:47 AM

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.

**Jhevon** · March 16th 2008, 10:56 AM

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

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