1. ## Laplace Transform?

Ned help with Laplace transform not sure what to do but have a idea

the question is find the Laplace transform of;
$\displaystyle te^{\text{-t}}cos(3t$) i think u gotta apply the therom $\displaystyle (-1)^nd^n/ds^n[F(s)]$
meaning it wil be the dervitive of the transform $\displaystyle e^{\text{-t}}cos(3t$) am i close :P lol

2. Originally Posted by zangestu888
Ned help with Laplace transform not sure what to do but have a idea

the question is find the Laplace transform of;
$\displaystyle te^{\text{-t}}cos(3t$) i think u gotta apply the therom $\displaystyle (-1)^nd^n/ds^n[F(s)]$
meaning it wil be the dervitive of the transform $\displaystyle e^{\text{-t}}cos(3t$) am i close :P lol

Yes that's correct, and to work out $\displaystyle \mathcal{L}\left\{e^{-t} \cos{3t}\right\}$

you need to use $\displaystyle \mathcal{L}\left\{e^{\lambda t}f(t)\right\} = \bar{f}\left(p-\lambda\right)$

and $\displaystyle \mathcal{L}\left\{ f(\mu t) \right\} = \frac{1}{\mu}\bar{f}\left(\frac{p}{\mu}\right)$

Good luck.

3. can i use the first shifting therom for $\displaystyle \mathcal{L}\left\{e^{-t} \cos{3t}\right\}$

4. Originally Posted by pomp
to work out $\displaystyle \mathcal{L}\left\{e^{-t} \cos{3t}\right\}$

you need to use $\displaystyle \mathcal{L}\left\{e^{\lambda t}f(t)\right\} = \bar{f}\left(p-\lambda\right)$
yep.

5. thanks my final answer i got was

$\displaystyle (s^2+4s-8)/(s^2+2s+10)^2$ can anyone please verify my transform? thank! you

6. - Wolfram|Alpha

Seems right