Question

For the function F (s) = (s+5)/s(s^2+2s+5), after splitting this function into the partial fractions, the co-efficient of 1/(s+1-j2) is?

(a) 1/2

(b) -1/2

(c) 1/4

(d) -1/4

I had been asked this question in a job interview.

This key question is from Inverse Transforms in portion Intoduction to the Laplace Transform of Network Theory

Answer 1

The correct answer is (b) -1/2

For explanation I would say: To obtain the constant B, multiply the given equation with (s+1-j2) and putting s = -1+j2. B = (s + 1 – j2)F (s)|s = (-1+j2) = (s+5)/s(s+1+j2)|s=-1+j2 = -1/2.