# Silly question about Laplace Transformations.

• Dec 3rd 2010, 08:07 AM
Silver
Say I have this term

$\displaystyle \frac{0.5}{s+2}$ ,

could I just say that 0.5 is a constant so it can be written as

$\displaystyle 0.5\cdot\frac{1}{s+2}$

and transform it normally, which would then be

$\displaystyle 0.5\cdot\exp^{-2t}$

or am I just being plain stupid and should know that things like this arent allowed with laplace terms?

I have been looking at examples, just cant seem to find any that would answer me :(
• Dec 3rd 2010, 08:11 AM
Silver
feeling pretty embarrased asking this question...
• Dec 3rd 2010, 09:19 AM
Ackbeet
You can definitely do that.
• Dec 4th 2010, 04:46 AM
HallsofIvy
$\displaystyle L(f)= \int_0^\infty e^{-st}f(t)dt$

So if f(t)= c u(t) where c is a constant,
$\displaystyle L(cu)= \int_0^\infty e^{-st}cu(t)dt= c\int_0^\infty e^{-st}u(t)dt= cL(u)$.
• Dec 4th 2010, 01:21 PM
Silver
Yeah, I actually figured when I was transforming my terms back, that by linearity I could take the constant out..