Question

What is the steady state value of F (t), if it is known that \(F(s) = \frac{2}{s(S+1)(s+2)(s+3)}\)?

(a) \(\frac{1}{2}\)

(b) \(\frac{1}{3}\)

(c) \(\frac{1}{4}\)

(d) Cannot be determined

I have been asked this question during an interview for a job.

My question is from Miscellaneous Examples on Fourier Series topic in division Fourier Series of Signals and Systems

Answer 1

Right answer is (b) \(\frac{1}{3}\)

The best I can explain: From the equation of F(s), we can infer that, a simple pole is at origin and all other poles are having negative real part.

∴ F(∞) = lim s→0 sF(s)

= lim s→0  \(\frac{2s}{s(S+1)(s+2)(s+3)}\)

= \(\frac{2}{s(S+1)(s+2)(s+3)}\)

= \(\frac{2}{6} = \frac{1}{3}\).