1
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 $${1 \over {2\pi }} < h < {1 \over \pi }$$ 2 GATE EE 2015 Set 2 MCQ (Single Correct Answer) +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. 3 GATE EE 2015 Set 2 MCQ (Single Correct Answer) +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 4 GATE EE 2015 Set 2 MCQ (Single Correct Answer) +2 -0.6 For the system governed by the set of equations: \eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = - 2{x_1} + u \cr & \,\,\,\,\,\,y = 3{x_1} \cr}
the transfer function $$Y(s)/U(s)$$ is given by
A
$$3\left( {s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
B
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
C
$$\left( {s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
D
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
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