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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
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