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1

### GATE EE 2017 Set 1

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 $$0$$
2

### GATE EE 2016 Set 1

The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$ in $$rad/s$$ is
A
$${\sqrt 3 }$$
B
$${1 \over {\sqrt 3 }}$$
C
$$3$$
D
$${3\sqrt 3 }$$
3

### GATE EE 2016 Set 1

The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\left( {2t + \phi } \right)$$ for the input $$\cos \left( {2t} \right).$$ The values of $$A$$ and $$\phi ,$$ respectively are
A
$${1 \over {\sqrt 2 }}, - {45^0}$$
B
$${1 \over {\sqrt 2 }}, + {45^0}$$
C
$$\sqrt 2 ,\, - {45^0}$$
D
$$\sqrt 2 ,\, + {45^0}$$
4

### GATE EE 2015 Set 1

A Bode magnitude plot for the transfer function $$𝐺(𝑠)$$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?
A
$${{1000\left( {s + 10} \right)} \over {s + 1000}}$$
B
$${{10\left( {s + 10} \right)} \over {s\left( {s + 1000} \right)}}$$
C
$${{s + 1000} \over {10s\left( {s + 10} \right)}}$$
D
$${{s + 1000} \over {10\left( {s + 10} \right)}}$$
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