The frequency response of a linear, time-invariant system is given by$$H(f) = frac{5}{1 + j 10 pi f}$$ The step response of the system is (GATE 2007 || EC || MCQ||1 MARK)

$$ frac{1}{5} (1 - e^{-5t}) u(t)$$

$$ frac{1}{5} (1 - e^{-t/5}) u(t)$$

Consider two transfer functions and $$G_1(s) = frac{1}{s^2 + as + b}$$$$G_2(s) = frac{s}{s^2 + as + b}$$The 3-dB bandwidths of their frequency responses are respectively,(GATE 2006 || EC || MCQ||1 MARK)

$$ sqrt{a^2 - 4b}, sqrt{a^2 - 4b}$$

$$ sqrt{a^2 - 4b}, sqrt{a^2 + 4b}$$

$$ sqrt{a^2 + 4b}, sqrt{a^2 - 4b}$$

$$ sqrt{a^2 + 4b}, sqrt{a^2 + 4b}$$

GATE EC|| CONTROL SYSTEM || FREQUENCY DOMAIN ANALYSIS|| PYQS(2000-2025)

Last Updated :

Discuss

Comments

Question 1

An amplifier with resistive negative feedback has two left-half plane poles in its open-loop transfer function. The amplifier

(GATE 2001 || EC || MCQ||1 MARK)

will always be unstable at high frequency
will be stable for all frequency
may be unstable, depending on the feedback factor
will oscillate at low frequency

Question 2

[2000 : 1 Mark]

Which one of the following polar diagrams corresponds to a lag network?

(GATE 2001 || EC || MCQ||1 MARK)

Question 3

In the system shown below, x(t) = (sin t)u(t). In a steady state, the response y(t) will be

(GATE 2006 || EC || MCQ||1 MARK)

[Tex]\frac{1}{\sqrt{2}} \sin \left( t - \frac{\pi}{4} \right)[/Tex]
[Tex]\frac{1}{\sqrt{2}} \sin \left( t + \frac{\pi}{4} \right)[/Tex]
[Tex]\frac{1}{\sqrt{2}} e^{-t} \sin t[/Tex]
[Tex]\sin t - \cos t[/Tex]

Question 4

The frequency response of a linear, time-invariant system is given by

[Tex]H(f) = \frac{5}{1 + j 10 \pi f}[/Tex]

The step response of the system is

(GATE 2007 || EC || MCQ||1 MARK)

[Tex]H(f) = \frac{5}{1 + j 10 \pi f}[/Tex]
[Tex]5(1 - e^{-t/5}) u(t)[/Tex]
[Tex]\frac{1}{5} (1 - e^{-5t}) u(t)[/Tex]
[Tex]\frac{1}{5} (1 - e^{-t/5}) u(t)[/Tex]

Question 5

Consider two transfer functions and

[Tex]G_1(s) = \frac{1}{s^2 + as + b}[/Tex]

[Tex]G_2(s) = \frac{s}{s^2 + as + b}[/Tex]

The 3-dB bandwidths of their frequency responses are respectively,

(GATE 2006 || EC || MCQ||1 MARK)

[Tex]\sqrt{a^2 - 4b}, \sqrt{a^2 + 4b}[/Tex]
[Tex]\sqrt{a^2 + 4b}, \sqrt{a^2 - 4b}[/Tex]
[Tex]\sqrt{a^2 - 4b}, \sqrt{a^2 - 4b}[/Tex]
[Tex]\sqrt{a^2 + 4b}, \sqrt{a^2 + 4b}[/Tex]

Question 6

Consider the pole-zero plot shown in the figure. Identify the type of filter represented by this pole-zero configuration.

Low pass filter
High pass filter
Band pass filter
Notch filter

Question 7

A system with a transfer function [Tex]G(s) = \frac{(s^2 + 9)(s + 2)}{(s + 1)(s + 3)(s + 4)}[/Tex]

is excited by sin(ωt). The steady-state output of the system is zero at

(GATE 2001 || EC || MCQ||1 MARK)

[Tex]\omega = 1[/Tex] rad/s
[Tex]\omega = 2[/Tex] rad/s
[Tex]\omega = 3[/Tex] rad/s
[Tex]\omega = 4[/Tex] rad/s

Question 8

The transfer function of a mass-spring-damper system is given by

[Tex]G(s) = \frac{1}{Ms^2 + Bs + K}[/Tex]

The frequency response data for the system are given in the following table.

Frequency	Magnitude (dB)	Phase (°)
0.01	-18.5	-0.2
0.1	-18.5	-1.3
0.2	-18.4	-2.6
1	-16.0	-16.9
2	-11.4	-89.4
3	-21.5	-151.0
5	-32.8	-167.0
10	-45.3	-174.5

The unit step response of the system approaches a steady-state value of ______.

(GATE 2015 || EC || MCQ||2 MARK)

0.12

Question 9

For a unity feedback control system with the forward path transfer function, the peak resonant magnitude M of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is.(GATE 2018 || EC || MCQ||2 MARK)

14.92

Question 10

A system with a transfer function

is subjected to an input 5 cos 3t. The steady-state output of the system is

The value of a is ……

(GATE 2005 || EC || MCQ||2 MARK)

Tags:

GATE

There are 14 questions to complete.

Take a part in the ongoing discussion