Question

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

• A. 0.5 rad/sec
• B. 1 rad/sec
• C. 2 rad/sec
• D. 4 rad/sec

Answer 1

The correct option is C 2 rad/sec

$T\left(s\right)=\frac{s^2+4}{(s+1)(s+4)}$

For frequency response, put $s=j\omega$

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

Magnitude of
$T\left(j\omega \right)=|T\left(j\omega \right)|=\frac{4-{\omega }^2}{\sqrt{(1+{\omega }^2)(16+\omega {)}^2}}=0$

$|T\left(j\omega \right)|=\frac{4-{\omega }^2}{\sqrt{(1+{\omega }^2)(16+\omega {)}^2}}=0$

$\omega =2rad/sec$

The system output is zero at 2 rad/sec.