1
GATE EE 2017 Set 2
+2
-0.6
The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the complex $$s$$-plane is
A
$$0 < K < 6$$
B
$$0 < K < 16$$
C
$$6 < K < 36$$
D
$$6 < K < 16$$
2
GATE EE 2016 Set 1
Numerical
+2
-0
Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which have real parts strictly less than $$-1$$ is _____________.
3
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 $${1 \over {2\pi }} < h < {1 \over \pi }$$
4
GATE EE 2014 Set 1
Numerical
+2
-0
For the given system, it is desired that the system be stable. The minimum value of $$\alpha$$ for this condition is _________