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

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likvau · Accepted Answer

(i)F(s)=2s+1s2−2s+1 2s+1(s−1)2=As−1+B(s−1)2 2s+1=As−1+B(s−1)2 2s+1=A(s−1)+B A=2,−A+B=1 B=3 F(s)=2s−1+3(s−1)2 f(t)=2et+3tet (ii)F(s)=3s+2s2−3s+2 3s+2(s−2)(s−1)=As−2+Bs−1 3s+2=A(s−1)+B(s−2) A+B=3 A=8,B=−5 −A−2B=2 F(s)=8s−2−5s−1 f(t)=8e2t−5et (iii)F(s)=3s2+4(s2+1)(s−1) 3s2+4(s−1)(s2+1)=As+Bs2+1+Cs−1 ⇒3s2+4=A(s2−s)+B(s−1)+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(s−1)

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

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