Question

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

(a) -1/4

(b) 1/4

(c) -1/2

(d) 1/2

The question was posed to me in an internship interview.

My query is from Inverse Transforms in section Intoduction to the Laplace Transform of Network Theory

Answer 1

The correct answer is (c) -1/2

Easiest explanation: 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.