H(s)=\frac{s-5}{(s-3)(s-1)} The inverse Laplace transform of H(s) is equal to f*g

Gage Potter 2022-05-01 Answered
H(s)=s5(s3)(s1)
The inverse Laplace transform of H(s) is equal to
fg
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Answers (1)

icebox2686zsd
Answered 2022-05-02 Author has 13 answers
Note that we can write
F(s)=s5s3=12s3
Then, f(t)=δ(t)2e3tu(t) and
h(t)=0tett(δ(t)2e3t)dt
=etet(e2t1)
=2ete3t
Note that partial fraction expansion makes things easier. We simply write
H(s)=2s11s3
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