# Laplace transform

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• May 25th 2007, 01:48 PM
PvtBillPilgrim
Laplace transform
Could someone show me how to do the following Laplace transform?

f(t) =
e^(2t) if 0 < t < 8
1 if t > 8

F(s) = ?

I'm pretty lost. Thanks for any help.
• May 25th 2007, 02:07 PM
CaptainBlack
Quote:

Originally Posted by PvtBillPilgrim
Could someone show me how to do the following Laplace transform?

f(t) =
e^(2t) if 0 < t < 8
1 if t > 8

F(s) = ?

I'm pretty lost. Thanks for any help.

Well we can do thus using just the definition of the Laplace Transform:

$
(\mathcal{L} f) (s) = \int_0^{\infty} f(t) e^{-st} dt
= \int_0^8 e^{2t}e^{-st} dt + \int_8^{\infty} e^{-st}dt
= \int_0^8 e^{t(2-s)} dt + \int_8^{\infty} e^{-st}dt
$

........ $=\frac{1}{s-2}[1-e^{8(2-s)}] + \frac{e^{-8s}}{s}$

RonL
• May 25th 2007, 02:25 PM
PvtBillPilgrim
Makes sense.
Thank you very much.