Question

If a characteristic equation of a closed-loop system is $s^2+2s+2=0$, then the system is

• A. overdamped
• B. critically damped
• C. underdamped
• D. undamped

Answer 1

The correct option is C underdamped

$S^2+2\xi {\omega }_n+{\omega }_n^2=0$
$2\xi {\omega }_n=2,\xi =\frac{1}{{\omega }_n}$
${\omega }_n=\sqrt{2}$
$\therefore \xi =\frac{1}{\sqrt{2}}$
$\because \xi <1$
Hence response will be underdamped.