Find the inverse Laplace transform f(t)=L^)-1 {F(s)} of each of the following functions.

Tabansi 2020-11-01 Answered

Find the inverse Laplace transform f(t)=L1{F(s)} of each of the following functions.
(i)F(s)=2s+1s22s+1
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
(ii)F(s)=3s+2s23s+2
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
(iii)F(s)=3s2+4(s2+1)(s1)
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.

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Expert Answer

likvau
Answered 2020-11-02 Author has 75 answers

(i)F(s)=2s+1s22s+1
2s+1(s1)2=As1+B(s1)2
2s+1=As1+B(s1)2
2s+1=A(s1)+B
A=2,A+B=1
B=3
F(s)=2s1+3(s1)2
f(t)=2et+3tet
(ii)F(s)=3s+2s23s+2
3s+2(s2)(s1)=As2+Bs1
3s+2=A(s1)+B(s2)
A+B=3
A=8,B=5
A2B=2
F(s)=8s25s1
f(t)=8e2t5et
(iii)F(s)=3s2+4(s2+1)(s1)
3s2+4(s1)(s2+1)=As+Bs2+1+Cs1
3s2+4=A(s2s)+B(s1)+C(s2+1)
A+B=3
A+B=0
B+C=4
A=12,B=12,C=72
F(s)=1s2(s2+1)12(s2+1)+72(s1)

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