2012
1.
The unilateral Laplace transform of f(t) is 1/(s2+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 = t2 – 1/2
c)
x = t2/2
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)
a1 ≠ 0,
a2 = 0, a3 = 0
b)
a1 = 0, a2 ≠
0, a3 ≠
0
c)
a1 = 0, a2 ≠
0, a3 = 0
d)
a1 ≠ 0,
a2 ≠ 0,
a3 = 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 Gc(s)=
(s+a)/(s+b).
6.
Gc(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
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