Question

For a second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

• A. $16$
• B. $4$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

The closed loop transfer funtion of the given system is

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{4}{s(s+4)+4}=\frac{4}{s^2+4s+4}$

Comparing with standard second order transfer function $\frac{K{\omega }_n^2}{s^2+2\xi {\omega }_n+{\omega }_n^2}$

$weget,{\omega }_n^2=4$

$or{\omega }_n=\sqrt{4}=2rad/sec$.