1
GATE EE 2003
MCQ (Single Correct Answer)
+2
-0.6
A control system with certain excitation is governed by the following mathematical equation $${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$\$
The natural time constants of the response of the system are
A
$$2s$$ and $$5s$$
B
$$3s$$ and $$6s$$
C
$$4s$$ and $$5s$$
D
$$1/3s$$ and $$1/6s$$
2
GATE EE 2003
MCQ (Single Correct Answer)
+2
-0.6
The roots of the closed loop characteristic equation of the system shown in fig is
A
$$-1$$ and $$-15$$
B
$$6$$ and $$10$$
C
$$-4$$ and $$-15$$
D
$$-6$$ and $$-10$$
3
GATE EE 2003
MCQ (Single Correct Answer)
+2
-0.6
The loop gain $$GH$$ of a closed loop system is given by the following expression $${K \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$ The value of $$K$$ for which the system just becomes unstable is
A
$$K=6$$
B
$$K=8$$
C
$$K=48$$
D
$$K=96$$
4
GATE EE 2003
MCQ (Single Correct Answer)
+2
-0.6
The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ gain at a frequency of $$\omega = 0.5a$$ are respectively
A
$${4.9^0},\,0.97\,dB$$
B
$${5.7^0},\,3\,dB$$
C
$${4.9^0},\,3\,dB$$
D
$${5.7^0},\,0.97\,dB$$
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