Laplace transformation problem

Question

There is a timely unchanged continuous function :

$$H(s)=\frac{s-1}{s+1}$$

At the entry of the system exists a $x(t)$ which Laplace's transformation is:

$$X(s)=\frac{(5s^2 - 15s + 7)}{(s-2)^3(s-1)}$$

Which is the impulse response?and which is the exit signal of the system?

Could someone show me the answers and elaborate me,on how this goes cause I have some clues but I am lacking i some aspects,Thanks in advance.

Welcome to math.SE! Please consider taking the time to read the [faq] to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers! — Daniel R, Sep 14 '13 at 09:14
Thank you very much both for the help. @ Mhenni Benghorbal :thanks nice edit,@ Daniel R : thanks for the links !!! — Phil_Charly, Sep 14 '13 at 09:23
Do you want to find the inverse Laplace of the two functions? — Mhenni Benghorbal, Sep 14 '13 at 09:31

score 1 · Accepted Answer · edited Sep 14 '13 at 10:59

Here is how you advance. Use partial fraction to get

$$H(s)=1-\frac{2}{1+s}$$

Taking the inverse Laplace gives

$$h(t)=\delta(t)-2e^{-t},$$

where $\delta(t)$ is the Dirac function. Note that, the Laplace transform of the functions $\delta(t)$ and $e^{-t}$ are $1$ and $\frac{1}{s+1}$. For the second one use partial fraction

$$X(s)= \frac{17}{\left( s-2 \right)^2} - \frac{17}{ \left( s-2 \right)} +\frac{17}{ \left( s-1 \right)}-\frac{27}{ \left( s-2 \right)^3} .$$

Now, try to finish the problem.

Laplace transformation problem

1 Answers1

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