Topic: Control Systems
The characteristic equation of a closed loop system is $s^{2}+2s+2=0$. Then the system is
- A. Over damped
- B. Centrally damped
- C. Under damped
- D. Un damped
Answer: C. Under damped
Explanation: The standard second-order characteristic equation is $s^2 + 2\zeta\omega_n s + \omega_n^2 = 0$.
Comparing this with $s^2 + 2s + 2 = 0$:
$\omega_n^2 = 2 \Rightarrow \omega_n = \sqrt{2} \approx 1.414$ rad/s.
$2\zeta\omega_n = 2 \Rightarrow \zeta = \frac{2}{2\omega_n} = \frac{1}{\sqrt{2}} \approx 0.707$.
Since the damping ratio $\zeta$ is between 0 and 1 ($0 < \zeta < 1$), the system is under damped.