# Laplace Transformation Question.

• Nov 11th 2009, 11:35 AM
Phyxius117
Laplace Transformation Question.
Not sure how to start this question -.-

Find the Laplace transform of the function:

f(t)=te^(2t)cos(2t)

http://webwork.geneseo.edu/webwork2_...144/char4C.pnghttp://webwork.geneseo.edu/webwork2_...144/char66.pngf(t)http://webwork.geneseo.edu/webwork2_...144/char67.png= ?

Thanks for the help!!
• Nov 11th 2009, 12:17 PM
pickslides
Hi there, been a while since i've done one of these, the definition is

$\mathcal{L}\left\{f(t)\right\}=\int_0^\infty e^{-st}f(t)~dt
$

Therefore

$\mathcal{L}\left\{te^{2t}cos(2t)
\right\}=\int_0^\infty e^{-st}te^{2t}\cos(2t)~dt=\int_0^\infty e^{t(2-s)}t\cos(2t)~dt
$

Also by the shift theorem

$\mathcal{L}\left\{e^{2t}\cos(2t)\right\}=\frac{s-2}{(s-2)^2+4}$
• Nov 11th 2009, 12:20 PM
Phyxius117
Ohhh I see now

I can use the the Theorem of Differentiation of transforms after that shift transformation.

Ima give it a try now!!
• Nov 11th 2009, 12:27 PM
Phyxius117
Thanks for the help!! I got the correct answer!!

It's

(s*(s-4))/((s^2-4s+8)^2)
• Nov 11th 2009, 12:29 PM
pickslides
Do you mean?

$\mathcal{L}\left\{t\times f(t)\right\}=-F'(s)
$
• Nov 11th 2009, 12:30 PM
pickslides
Quote:

Originally Posted by Phyxius117