# Math Help - Laplace Transformation Question.

1. ## Laplace Transformation Question.

Not sure how to start this question -.-

Find the Laplace transform of the function:

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

f(t)= ?

Thanks for the help!!

2. 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

$\mathcal{L}\left\{e^{2t}\cos(2t)\right\}=\frac{s-2}{(s-2)^2+4}$

3. Ohhh I see now

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

Ima give it a try now!!

4. Thanks for the help!! I got the correct answer!!

It's

(s*(s-4))/((s^2-4s+8)^2)

5. Do you mean?

$\mathcal{L}\left\{t\times f(t)\right\}=-F'(s)
$

6. Originally Posted by Phyxius117