1
GATE ECE 2014 Set 2
Numerical
+1
-0
The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.
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2
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
For the following system, GATE ECE 2014 Set 2 Control Systems - Signal Flow Graph and Block Diagram Question 11 English When X1(s) = 0 , the transfer function $$\frac{\mathrm Y\left(\mathrm s\right)}{{\mathrm X}_2\left(\mathrm s\right)}$$ is
A
$$\frac{\mathrm s+1}{\mathrm s^2}$$
B
$$\frac1{\mathrm s+1}$$
C
$$\frac{\mathrm s+2}{\mathrm s\left(\mathrm s+1\right)}$$
D
$$\frac{\mathrm s+1}{\mathrm s\left(\mathrm s+2\right)}$$
3
GATE ECE 2014 Set 2
Numerical
+2
-0
The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. GATE ECE 2014 Set 2 Control Systems - Frequency Response Analysis Question 16 English

If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is

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4
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
An unforced linear time invariant (LTI) system is represented by $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$$

If the initial conditions are x1(0)= 1 and x2(0)=-1, the solution of the state equation is

A
$${x_1}\left( t \right) = - 1,{x_2}\left( t \right) = 2$$
B
$${x_1}\left( t \right) = - {e^{ - t}},{x_2}\left( t \right) = 2{e^{ - t}}$$
C
$${x_1}\left( t \right) = {e^{ - t}},{x_2}\left( t \right) = - {e^{ - 2t}}$$
D
$${x_1}\left( t \right) = {e^{ - t}},{x_2}\left( t \right) = - 2{e^{ - t}}$$
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