Question

The transfer function of a system is given as $\frac{100}{s^2+20s+100}.$ The system is

• A. An overdamped system
• B. An underdamped system
• C. A critically damped system
• D. An unstable system

Answer 1

The correct option is C A critically damped system

$M\left(s\right)=\frac{100}{s^2+20s+100}$

Comparing with standard form,

$M\left(s\right)=\frac{{\omega }_n^2}{s^2+2\xi {\omega }_{n}s+{\omega }_n^2}$

$\therefore 2\xi {\omega }_n=20$

${\omega }_n=10$

$\therefore \xi =1$

$\therefore$ The system is critically damped.