Types of Second Order Systems

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

1. overdamped
2. critically damped
3. underdamped
4. undamped

Q. Consider a system with the transfer function $G\left(s\right)=\frac{s+6}{K{s}^2+s+6}$. Its damping ratio will be $0.5$ when the value of $K$ is

1. $2/6$
2. $3$
3. $1/6$
4. $6$

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

1. An overdamped system
2. An underdamped system
3. A critically damped system
4. An unstable system

Q. For a second order system, damping ratio $\left(\xi \right)$, is $0<\xi <1$, then the roots of the characteristic polynomial are

1. real but not equal
2. real and equal
3. complex conjugates
4. imaginary

Q. A control system with damping ratio $\xi =\sqrt{3}$ is represented by the block diagram which employs proportional plus error rate control. The value of error rate constant K when unit step is given as input to system will be

1. $\frac{1}{3}$
2. $\frac{1}{2}$
3. $\frac{1}{4}$
4. $\frac{2}{3}$

Q. Match the transfer function of the second-order system with the nature of the system given below.

$\begin{array}{cc}Transferfunction& Natureofsystem\\ P.\frac{15}{s^2+5s+15}& I.Overdamped\\ Q.\frac{25}{s^2+10s+25}& II.Criticallydamped\\ R.\frac{35}{s^2+18s+35}& III.Underdamped\end{array}$

Codes:

1. P-I, Q-II, R-III
2. P-II, Q-I, R-III
3. P-III, Q-II, R-I
4. P-III, Q-I, R-II

Q. For a second order system, damping ratio $\left(\xi \right)$, is $0<\xi <1$, then the roots of the characteristic polynomial are

1. real but not equal
2. real and equal
3. complex conjugates
4. imaginary