X(s)=((5s^2−15s+7))/((s−2)^3(s−1)). Which is the impulse response?and which is the exit signal of the system?

Ty Moore 2022-11-18 Answered
There is a timely unchanged continuous function :
H ( s ) = s 1 s + 1
At the entry of the system exists a x(t) which Laplace's transformation is:
X ( s ) = ( 5 s 2 15 s + 7 ) ( s 2 ) 3 ( s 1 )
Which is the impulse response?and which is the exit signal of the system?
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Answers (1)

gortepap6yb
Answered 2022-11-19 Author has 19 answers
Here is how you advance. Use partial fraction to get
H ( s ) = 1 2 1 + s
Taking the inverse Laplace gives
h ( t ) = δ ( t ) 2 e t ,
where δ ( t ) is the Dirac function. Note that, the Laplace transform of the functions δ ( t ) and e t are 1 and 1 s + 1 . For the second one use partial fraction
X ( s ) = 17 ( s 2 ) 2 17 ( s 2 ) + 17 ( s 1 ) 27 ( s 2 ) 3 .
Now, try to finish the problem.
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