# Laplace trnasform, Final in 4hours! please help!

Printable View

• Dec 17th 2008, 01:46 AM
AmyZheng
Laplace trnasform, Final in 4hours! please help!
how do you derive the laplace transform for t^2 sin(3t)?
• Dec 17th 2008, 01:52 AM
Mush
$\mathcal L (t^2 sin(3t)) = \int_0^{\infty} t^2sin(3t)e^{-st} dt$

I'm afraid it's a rather long and boring integration by parts.
• Dec 17th 2008, 04:00 AM
mr fantastic
Quote:

Originally Posted by AmyZheng
how do you derive the laplace transform for t^2 sin(3t)?

Use the following operational theorem:

$LT[t^2 \, f(t)] = F''(s)$ where $LT[f(t)] = F(s)$.

In your case $f(t) = \sin (3t) \Rightarrow F(s) = \frac{3}{s^2 + 3^2}$.