Topic: Electronics Engineering
The characteristics equation of a closed loop control system is given as $s^{2}+4s+16=0.$ The resonant frequency in radian/sec of the system is
- A. 2
- B. $2\sqrt{3}$
- C. 4
- D. $2\sqrt{2}$
Answer: D. $2\sqrt{2}$
Explanation: $s^{2}+4s+16=0$
$\omega_{n}^{2} = 16 \Rightarrow \omega_{n} = 4$
$2\xi\omega_{n}=4 \Rightarrow 2\xi\times4=4 \Rightarrow \xi=0.5$
$\omega_{r}=\omega_{n}\sqrt{1-2\xi^{2}} = 4\sqrt{1-2(0.5)^{2}} = 4\sqrt{0.5} = 2\sqrt{2}$