1
GATE EE 2022
+1
-0.33

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is $$-$$180$$^\circ$$. This system has

A
one LHP pole and one RHP zero at the same frequency.
B
one LHP pole and one LHP zero at the same frequency.
C
two LHP poles and one RHP zero.
D
two RHP poles and one LHP zero.
2
GATE EE 2022
+1
-0.33

An LTI system is shown in the figure where $$G(s) = {{100} \over {{s^2} + 0.1s + 100}}$$. The steady state output of the system, to the input r(t), is given as y(t) = a + b sin(10t + $$\theta$$). The values of a and b will be

A
a = 1, b = 10
B
a = 10, b = 1
C
a = 1, b = 100
D
a = 100, b = 1
3
GATE EE 2022
+1
-0.33

The open loop transfer function of a unity gain negative feedback system is given as

$$G(s) = {1 \over {s(s + 1)}}$$

The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point ($$-$$1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

A
0
B
1
C
2
D
3
4
GATE EE 2017 Set 1
+1
-0.3
The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$

Let the output of the system be $${v_0}\left( t \right) = {v_m}\sin \left( {\omega t + \phi } \right)$$ for the input $${v_i}\left( t \right) = {v_m}\sin \left( {\omega t} \right).$$ Then the minimum and maximum values of ϕ (in radians) are respectively

A
$${{ - \pi } \over 2}\,$$ and $${{ \pi } \over 2}\,$$
B
$${{ - \pi } \over 2}\,$$ and $$0$$
C
$$0$$ and $${{ \pi } \over 2}\,$$
D
$${ - \pi }$$ and $$0$$
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