Question

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)t

The 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 1

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.