1
GATE EE 2015 Set 2
+2
-0.6
The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given by which one of the following waveforms?
A
B
C
D
2
GATE EE 2015 Set 2
+2
-0.6
The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $$𝑥$$ and $$𝑦.$$ The integration time step is $$h.$$ $${{{x_{k + 1}} - {x_k}} \over h} = {y_k},\,\,\,\,\,{{{y_{k + 1}} - {y_k}} \over h} = {x_k}$$\$

For this discrete-time system, which one of the following statements is TRUE?

A
The system is not stable for $$h>0$$
B
The system is stable for $$h > {1 \over \pi }$$
C
The system is stable for $$0 < h < {1 \over {2\pi }}$$
D
The system is stable for $${1 \over {2\pi }} < h < {1 \over \pi }$$
3
GATE EE 2015 Set 2
+2
-0.6
An open loop transfer function $$G(s)$$ of system is $$G\left( s \right) = {k \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

A
$$-0.42$$
B
$$-1.58$$
C
$$0.42$$ and $$-1.58$$
D
none of the above.
4
GATE EE 2015 Set 2
+1
-0.3
Nyquist plots of two functions $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ are shown in figure.

Nyquist plot of the product of $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ is

A
B
C
D
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