# Laplace/Inverse Laplace Questions

• Aug 14th 2010, 07:38 AM
redskies
Laplace/Inverse Laplace Questions
I have to find Laplace transform of:

$\displaystyle \frac{1}{4}t^7e^\frac{-1t}{2}$

Here is what I have:

$\displaystyle \frac{1}{4}\frac{7!}{s^8}\frac{1}{s+\frac{1}{2}}$

which simplifies to:

$\displaystyle \frac{1260}{s^8(s+\frac{1}{2})}$

Is this ok??

Also, I have to find inverse Laplace of:

$\displaystyle \frac{-8}{(s-7)^5}$

Do I need to use partial fractions on this, or is there a simpler way?

Thanks
• Aug 14th 2010, 09:32 AM
Ackbeet
I think you're not using the LT theorems correctly. Perhaps you're inverting the order of application? I get $\displaystyle 1260/(s+1/2)^8$.

For your inverse LT, I would use the shifting theorem first, and then the nth power theorem.
• Aug 14th 2010, 11:29 AM
chisigma
For both questions I soggest You to remember one of the basic properties of the Laplace Tranform...

$\displaystyle \displaystyle \mathcal{L} \{f(t)\} = F(s) \rightarrow \mathcal{L}\{f(t) \ e^{a t}\} = F(s-a)$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$