Laplace/Inverse Laplace Questions

**redskies** · August 14th 2010, 07:38 AM

I have to find Laplace transform of:

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

Here is what I have:

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

which simplifies to:

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

Is this ok??

Also, I have to find inverse Laplace of:

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

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

Thanks

**Ackbeet** · August 14th 2010, 09:32 AM

I think you're not using the LT theorems correctly. Perhaps you're inverting the order of application? I get $1260/(s+1/2)^8$ .

For your inverse LT, I would use the shifting theorem first, and then the nth power theorem.

**chisigma** · August 14th 2010, 11:29 AM

For both questions I soggest You to remember one of the basic properties of the Laplace Tranform...

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

Kind regards

$\chi$ $\sigma$

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