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1

GATE EE 2011

The response $$h(t)$$ of a linear time invariant system to an impulse $$\delta \left( t \right),$$ under initially relaxed condition is $$h\left( t \right) = \,{e^{ - t}} + {e^{ - 2t}}.$$ The response of this system for a unit step input $$u(t)$$ is
A
$$u\left( t \right) + {e^{ - t}} + {e^{ - 2t}}$$
B
$$\left( {{e^{ - t}} + {e^{ - 2t}}} \right)u\left( t \right)$$
C
$$\left( {1.5 - {e^{ - t}} - 0.5{e^{ - 2t}}} \right)u\left( t \right)$$
D
$${e^{ - t}}\delta \left( t \right) + {e^{ - 2t}}u\left( t \right)$$
2

GATE EE 2011

A two-loop position control system is shown below.
The gain $$k$$ of the Tacho-generator influences mainly the
A
Peak overshoot
B
Natural frequency of oscillation
C
Phase shift of the closed loop transfer function at very low frequencies $$\left( {\omega \to \infty } \right)$$
D
Phase shift of the closed loop transfer function at very low frequencies $$\left( {\omega \to \infty } \right)$$
3

GATE EE 2009

The unit - step response of a unity feedback system with open loop transfer function $$G\left( s \right) = {K \over {\left( {s + 1} \right)\left( {s + 2} \right)}}$$ is shown in the figure. The value of $$K$$ is
A
$$0.5$$
B
$$2$$
C
$$4$$
D
$$6$$
4

GATE EE 2008

The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$

The steady state value of the output of the system for a unit impulse input applied at time instant $$t=1$$ will be

A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
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