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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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#### Questions Asked from Time Response Analysis

On those following papers in Marks 2
Number in Brackets after Paper Indicates No. of Questions
GATE EE 2015 Set 2 (1)
GATE EE 2013 (1)
GATE EE 2011 (2)
GATE EE 2009 (1)
GATE EE 2008 (2)
GATE EE 2007 (3)
GATE EE 2005 (2)
GATE EE 2004 (2)
GATE EE 2003 (3)
GATE EE 2000 (1)
GATE EE 1996 (2)
GATE EE 1991 (1)

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NEET

Class 12