Basics of Nyquist Plot

Q. The Nyquist plot for the open-loop transfer function $G\left(s\right)$ of a unity negative feedback system is shown in the figure, if $G\left(s\right)$ has no pole in the right-half of s-plane, the number of roots of the system characteristic equation in the right-half of s-plane is

1. $0$
2. $1$
3. $2$
4. $3$

Q. The Nyquist plot of a loop transfer function $G\left(j\omega \right)H\left(j\omega \right)$ of a system encloses the $(-1,0)$ point. The gain margin of the system is

1. less than zero
2. zero
3. greater than zero
4. infinity

Q. The number and direction of encirclements around the point $-1+j0$ in the complex plane by the Nyquist plot of
$G\left(s\right)=\frac{1-s}{4+2s}is$

1. zero
2. one, anti-clockwise
3. one, clockwise
4. two, clockwise

Q.

The number of times the Nyquist plot of
$G\left(s\right)=\frac{s-1}{s+1}$
will encircle the origin clockwise is

1. 1

Q. Which of the following is the transfer function of a system having the Nyquist plot shown in figure below?

1. $\frac{K}{s(s+2{)}^2(s+5)}$
2. $\frac{K}{s^2(s+2)(s+5)}$
3. $\frac{K(s+1)}{s^2(s+2)(s+5)}$
4. $\frac{K(s+1)(s+3)}{s^2(s+2)(s+5)}$

Q. The pole-zero map of a rational function $G\left(s\right)$ is shown below. When the closed counter $r$ is mapped into the $G\left(s\right)-plane$, then the mapping encircles.

1. the point $-1+j0$ of the $G\left(s\right)-plane$ once in the counter-clockwise direction
2. the origin of the $G\left(s\right)-plane$ once in the clockwise direction
3. the origin of the $G\left(s\right)-plane$ once in the counter clockwise direction
4. the point $-1+j0$ of the $G\left(s\right)-plane$ once in the clockwise direction

Q. Nyquist plots of two fucntions $G_1\left(s\right)$ and $G_2\left(s\right)$ are shown in figure.

Nyquist plot of the product of $G_1\left(s\right)$ and $G_2\left(s\right)$ is

1. 
2. 
3. 
4. 

Q.

Consider the statndard negative feedback configuration with
$G\left(s\right)=\frac{s^2+0.2s+100}{s^2-0.2s+100}andH\left(s\right)=\frac{1}{2}.$
The number of clockwise encirclements of (-1, 0) in the Nyquist plot of the Loop transfer-function G(s) H(s) is

1. 0

Q. For the transfer function $G\left(j\omega \right)=5+j\omega$, the corresponding Nyquist plot for positive frequency has the form

1. 
2. 
3. 
4.