Question

A second -order system has the transfer function $\frac{C\left(s\right)}{R\left(s\right)}=\frac{4}{s^2+4s+4}$. With $r\left(t\right)$ as the unit-step function, the response $c\left(t\right)$ of the system is represented by

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{4}{s^2+4s+4}$
$2\xi {\omega }_n=4,{\omega }_n=2$
$\therefore \xi =1$ (Critical damping)
$t_s=\frac{4}{\xi {\omega }_n}=\frac{4}{1\times 2}=2$