1
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The output of a standard second–order system for a unit step input is given as $$$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}\cos\left(\sqrt3t\;-\;\frac{\mathrm\pi}6\right)$$$ The transfer function of the system is
A
$$\frac2{\left(s+2\right)\left(s+\sqrt3\right)}$$
B
$$\frac1{s^2+2s+1}$$
C
$$\frac3{s^2+2s+3}$$
D
$$\frac4{s^2+2s+4}$$
2
GATE ECE 2015 Set 2
Numerical
+2
-0
The transfer function of a mass-spring damper system is given by $${\rm{G(s) = }}{1 \over {M{s^2} + Bs + K}}$$ The frequency response data for the system are given in the following table. GATE ECE 2015 Set 2 Control Systems - Frequency Response Analysis Question 15 English The unit step response of the system approaches a steady state value of ______.
Your input ____
3
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The state variable representation of a system is given as $$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \left[ {\matrix{ 1 \cr 0 \cr } } \right] \cr & y = \left[ {\matrix{ 0 & 1 \cr } } \right]x \cr} $$$

The response y(t) is

A
sin(t)
B
1-et
C
1-cos(t)
D
0
4
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the product of sums given below is equal to the funtion F(X, Y, Z)?
A
$$(\overline X + \overline Y + \overline Z ).(\overline X + Y + Z).(X + \overline Y + \overline Z )$$
B
$$(X + Y + Z).(X + \overline Y + \overline Z ).(\overline X + Y + Z)$$
C
$$(\overline X + \overline Y + Z).(\overline X + Y + \overline Z ).(X + \overline Y + Z).(X + Y + \overline Z ).(X + Y + Z)$$
D
$$(X + Y + \overline Z ).(\overline X + Y + Z).(\overline X + Y + \overline Z ).((\overline X + \overline Y + Z).(\overline X + \overline Y + \overline Z )$$
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