Question

A system transfer function

\(G\left( s \right) = \frac{{\left( {{s^2} + 9} \right)\left( {s + 2} \right)}}{{\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}}\)

is excited by sin(ωt). The steady state output of system is zero at

1. ω = 1 rad/sec
2. ω = 3 rad/sec
3. ω = 2 rad/sec
4. ω = 4 rad/sec

Answer 1

Correct Answer - Option 2 : ω = 3 rad/sec

\(\;\sin \omega t \to \boxed{G\left( s \right)} \to Y\left( s \right) = \left| {G\left( s \right)} \right| \cdot \sin \left( {\omega t + \angle G\left( s \right)} \right)\)

Output will be zero when

|G(s)| = 0

Put s = jω

\(\left| {\frac{{\left( { - {\omega ^2} + 9} \right)\left( {j\omega + 2} \right)}}{{\left( {j\omega + 1} \right)\left( {j\omega + 3} \right)\left( {j\omega + 4} \right)}}} \right| = 0\)

at         ω = 3   , |G(jω)| = 0