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1

GATE EE 2003

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

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

The block diagram shown in fig given is a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is
A
$$25\%$$
B
$$0.75\%$$
C
$$6\%$$
D
$$33\%$$
4

GATE EE 2000

A unity feedback system has open-loop transfer function $$G\left( s \right) = {{25} \over {s\left( {s + 6} \right)}}.$$ The peak overshoot in the step-input response of the system is approximately equal to
A
$$5\%$$
B
$$10\%$$
C
$$15\%$$
D
$$20\%$$
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