Laplace Transform?

**zangestu888** · July 13th 2009, 09:21 PM

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

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

**pomp** · July 13th 2009, 09:39 PM

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

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

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

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

Good luck.

**zangestu888** · July 13th 2009, 09:40 PM

can i use the first shifting therom for $<br /> <br /> \mathcal{L}\left\{e^{-t} \cos{3t}\right\}<br />$

**pomp** · July 13th 2009, 09:43 PM

Originally Posted by pomp

to work out $\mathcal{L}\left\{e^{-t} \cos{3t}\right\}$

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

yep.

**zangestu888** · July 14th 2009, 12:22 PM

thanks my final answer i got was

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

**pomp** · July 14th 2009, 05:27 PM

- Wolfram|Alpha

Seems right

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