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1

### GATE EE 2015 Set 2

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 $${1 \over {2\pi }} < h < {1 \over \pi }$$
2

### GATE EE 2014 Set 2

Numerical
A system with the open loop transfer function $$G\left( s \right) = {K \over {s\left( {s + 2} \right)\left( {{s^2} + 2s + 2} \right)}}$$ is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of $$K$$ is ________.

3

### GATE EE 2014 Set 1

Numerical
For the given system, it is desired that the system be stable. The minimum value of $$\alpha$$ for this condition is _________

Correct answer is between 0.61 and 0.63
4

### GATE EE 2012

The feedback system shown below oscillates at $$2$$ rad/s when
A
$$K=2$$ and $$a=0.75$$
B
$$K=3$$ and $$a=0.75$$
C
$$K=4$$ and $$a=0.5$$
D
$$K=2$$ and $$a=0.5$$
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