**2013**

1.
The Bode plot of a transfer function G(s) is shown in the figure
below.

The
gain (20log|G(s)|) is 32 dB and – 8 dB at 1 rad/sec and 10 rad/sec
respectively. The phase is negative for all ω.
Then G(s) is

a)
39.8/s

b)
39.8/s

^{2}
c)
32/s

d)
32/s

^{2}**
**

**Solution :**https://www.youtube.com/watch?v=YkPfY-Gufmg

2.
Which one of the following is NOT TRUE for a continuous time causal
and stable LTI system?

a)
all the poles of the system must lie on the left side of the jω
axis

b)
zeros of the system can lie anywhere in the s-plane

c)
all the poles must lie with in |s| = 1

d)
all the roots of the characteristic equation must be located on the
let side of the jω axis

**
**

**Solution :**https://www.youtube.com/watch?v=pKt_YzAm3z0

3.
A polynomial f(x) = a

_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x–a_{0}with all coefficients positive has
a)
no real roots

b)
no negative real root

c)
odd number of real roots

d)
at least one positive and one negative real root

**
**

**Solution :**

4.
Assuming zero initial conditions, the response y(t) of the system
given below for a unit step input, u(t) is __________________

a)
u(t)

b)
t.u(t)

c)
(1/2)t

^{2}.u(t)
d)
e

^{-t}.u(t)**
**

**Solution :**https://www.youtube.com/watch?v=haTwaJVl46E

5.
The transfer function V

_{2}(s)/V_{1}(s) of the circuit shown is**
**

**Solution :**https://www.youtube.com/watch?v=iVJ4qUlg8BE

6.
The open loop transfer function of a DC motor is given as ω(s)/V

The
approximate value of K_{a}(s) = 10/(1+10s). when connected in feedback as shown below._{a}that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open loop system is

a)
1

b)
5

c)
10

d)
100

**
**

**Solution :**https://www.youtube.com/watch?v=594vhbYCvbs

7.
A system is described by the differential equation
d

^{2}y/dt^{2}+5dy/dt+6y(t) = x(t). Let x(t) be a rectangular pulse given as x(t) = 1 for 0<t<2 and zero otherwise. Assuming that y(0) = 0 and dy/dt = 0 at t=0, then the Laplace transform of y(t) is**
**

**Solution :**https://www.youtube.com/watch?v=Z6o8dcPFVgI

8.
The signal flow graph for a system is given below.

The transfer
function Y(s)/U(s) for this system is**
**

**Solution :**https://www.youtube.com/watch?v=ndeVYkf7j6w

9.
The state diagram of the system is shown below. A system is
described by the state variable equations

a.
State variable equations of the system shown in the above figure is

**
**

b.
The state transition matrix e

^{At}of the system shown in the figure above is**
**

**Solution (a & b) :**https://www.youtube.com/watch?v=wnfqGfnPFcs