Question

Given a system function H(s) = \(\frac{1}{s+10}\). Let us consider a signal sin 10t. Then the steady state response is ___________

(a) 1

(b) 2

(c) 0

(d) 5

I had been asked this question in a national level competition.

My question is based upon Advanced Problems on Filters topic in chapter Filters and Attenuators of Network Theory

Answer 1

Right option is (c) 0

For explanation I would say: H(s) = \(\frac{V(s)}{J(s)}\)

= \(\frac{1}{s+10}\)

V(s) = \(\frac{1}{s+10}\) . J(s)

J(s) = L (sin 10t) = \(\frac{10}{s^2+100}\)

V (s) = \(\frac{1}{s^2+100} . \frac{10}{s+10}\)

VSS = lims→0⁡ sV(s)

= 0.