2011

1.
The differential equation 100d

^{2}y/dt^{2}-20dy/dt+y = x(t) describes a system with an input x(t) and an output y(t).The system which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform**
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**Solution :**https://www.youtube.com/watch?v=nGDKxd0P1DA

2.
for the transfer function G(jω)
= 5 + jω, the corresponding Nyquist plot for positive frequency has
the form

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**Solution :**https://www.youtube.com/watch?v=F0oR9sCCy80

3.
The root locus plot for a system is given below. The open loop
transfer function corresponding to this plot is given by

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**Solution :**https://www.youtube.com/watch?v=ARZuGJ_JqBo

4.
The block diagram of a system with one input u and two outputs y

A state space model of the system in terms of the
state vector ẋ
and the vector ẏ
= [y_{1}and y_{2}is given below._{1}y

_{2}]

^{T}is

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**Solution :**https://www.youtube.com/watch?v=CsciojvPQF8

5.
If F(s) = L[f(t)] = 2(s+1)/(s

^{2}+4s+7), then the initial and final values of f(t) are respectively
a)
0,2

b)
2,0

c)
0,2/7

d)
2/7,0

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**Solution :**https://www.youtube.com/watch?v=Eq8IxIWokfo

**Common Data Questions 6 & 7:**

The
input – output transfer function of a plant H(s) = 100/s(s+10)

^{2}. The plant is placed in a unity negative feedback configuration as shown in figure below.
6.
The signal flow graph that DOES NOT model the plant transfer function
H(s) is

**
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**Solution :**https://www.youtube.com/watch?v=gSg5jPv06fQ

7.
The gain margin of the system under closed loop unity negative
feedback is

a)
0 dB

b)
20 dB

c)
26 dB

d)
46 dB

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**Solution :**https://www.youtube.com/watch?v=HreyReFPqag

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