L^{-1}bigg(frac{5}{s^{2}(s^{2}-4s+5)}bigg)=5int_{0}^{infty}(t-T)e^{2T}sin 2T dT Select one: True or False

snowlovelydayM 2021-03-09 Answered
L1(5s2(s24s+5))=50(tT)e2Tsin2T dT
Select one: True or False
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Expert Answer

Laith Petty
Answered 2021-03-10 Author has 103 answers

Step 1
Given:
Let us consider,
L1(5s2(s24s+5))
Step 2
L1(5s2(s24s+5))
=L1(5s21s24s+5)
Let us consider,
H(s)=5s2
By Applying the inverse laplace transform as below,
L1(H(s))=5L1(1s2)
h(t)=5t
Step 3
Let us consider,
G(s)=1s24s+5
G(s)=1s24s+4+1
G(s)=1(s2)2+1
By Applying the inverse Laplace Transform, 
L1(G(s))=L1(1(s2)2+1)
=e2tsint
Step 4
L1(H(s)G(s))=0h(tT)g(T)
Therefore, 
L1(5s2(s24s+5))=50(tT)e2TsinT
Hence ,
The given Equation is False.

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