System Response 1.2

Ask

A system with zero initial conditions has the closed loop transfer function $ T(s) = \frac{s^2 +4}{(s+1)(s+4)}$.The system output is zero at the frequency______rad/s

(a) 2

(b) 1

(c) 0

(d) none of above

Answer is ( a )

Concept

The transfer function of system is $T(s) = \frac{s^2+4}{(s+1)(s+4)} $

$T(j\omega) = \frac{(j\omega)^{2}+4}{(j\omega+1)(j\omega+4)} $

If system output is zero, $|T(j\omega)| = \frac{|4-\omega^2|}{|(j\omega+4)(j\omega+1|} = 0 $

$ - \omega^2 + 4 = 0, \omega = 2 rad/sec $