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For the function F (s) = (s+5)/s(s^2+2s+5), after splitting this function into the partial fractions. What is the inverse transform of F (s) is?(a) 1+ 1/2 e^(-1+j2)t-1/2 e^(-1-j2)t(b) 1+ 1/2 e^(-1+j2)t+1/2 e^(-1-j2)t(c) 1- 1/2 e^(-1+j2)t-1/2 e^(-1-j2)t(d) 1- 1/2 e^(-1+j2)t+1/2 e^(-1-j2)tThe question was asked in an international level competition.Enquiry is from Inverse Transforms topic in section Intoduction to the Laplace Transform of Network Theory

Answer» RIGHT answer is (c) 1- 1/2 E^(-1+j2)t-1/2 e^(-1-j2)t

The best explanation: The inverse transform F(s) is f(t), f (t) = L-1(F (s)) = L-1(1/s-1/2(s+1-j2) – 1/2(s+1+j2)) = 1-1/2 e^(-1+j2)t-1/2 e^(-1-j2)t.


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