2012

1.
The unilateral Laplace transform of f(t) is 1/(s

^{2}+s+1). The unilateral transform of t.f(t) is**
**

**Solution :**https://www.youtube.com/watch?v=91xwp0WF7Lw

2.
With initial condition x(1) = 0.5, the solution of the differential
equation, t.(dx/dt)+x = t is

a)
x = t – 1/2

b)
x = t

^{2}– 1/2
c)
x = t

^{2}/2
d)
x = t/2

**
**

**Solution :**https://www.youtube.com/watch?v=G2uWH7-U30w

3.
A system with transfer function is excited by sin(ωt).

a)
ω = 1 rad/sec

b)
ω = 2 rad/sec

c)
ω = 3 rad/sec

d)
ω = 4 rad/sec

**
**

**Solution :**https://www.youtube.com/watch?v=UYEEuh71lxc

4.
The feedback system shown below oscillates at 2 rad/sec, when

a)
K = 2 and a = 0.75

b)
K = 3 and a = 0.75

c)
K = 4 and a = 0.5

d)
K = 2 and a = 0.5

**
**

**Solution :**https://www.youtube.com/watch?v=IBPC5lyX_X4

5.
The state variable description of an LTI system is by

where
y is the output and u is the input. The system is controllable for

a)
a

_{1}≠ 0, a_{2}= 0, a_{3}= 0
b)
a

_{1}= 0, a_{2}≠ 0, a_{3}≠ 0
c)
a

_{1}= 0, a_{2}≠ 0, a_{3}= 0
d)
a

_{1}≠ 0, a_{2}≠ 0, a_{3}= 0**
**

**Solution :**https://www.youtube.com/watch?v=dPCv96oD6Ow

**Statement for Linked Answer Questions : 6 and 7**

The
transfer function of a compensator is given as G

_{c}(s)= (s+a)/(s+b).
6.
G

_{c}(s) is a lead compensator if
a)
a = 1, b =2

b)
a = 3, b =2

c)
a = –3, b = –1

d)
a = 3, b =1

**
**

7.
The phase of the above lead compensator is maximum at

a)
√2 rad/sec

b)
√3 rad/sec

c)
√6 rad/sec

d)
1/√3 rad/sec

**
**

**Solution (6 & 7) :**https://www.youtube.com/watch?v=CSWEFDPoSsA