1. For the following differential equation

2d2y

dt2+ 4

dy

dt+ 8y = 8x

the damping ratio is

A. 1

B. 2

C. 0.5

D. 0.7

Solution: Let x be the input and y be the output.

d2y

dt2+ 2

dy

dt+ 4y = 4x

Taking Laplace transfrom

s2Y (s) + 2sY (s) + 4Y (s) = 4X(s)

The transfer function of the system is given by

Y (s)

X(s)=

4

s2 + 2s + 4

Comparing with the standard form

Y (s)

X(s)=

ω2n

s2 + 2ζω2ns + ω2

n

Therefore, ωn = 2.

2ζωn = 2

ζωn = 1

ζ =1

ωn

=1

2= 0.5

2. The time constant for the differential equation in the above problem is

A. 0.5

B. 1.5

C. 0.2

D. 1.0

Solution: Time constant T = 1

ζωn= 1

3. The open-loop transfer function of a system is

H(s)G(s) =10

s(s + 2)(s + 5)

The system is of type

A. N=0

B. N=1

C. N=2

D. N=3

Solution: The type of a system is the number of poles at the origin.

4. Which of the following is used for Nyquist plot?

A. Characteristic equation

B. Open-loop transfer function

C. Closed-loop transfer function

D. None of these

Solution: Used to determine the stability of closed-loop systems on the basis ofopen-loop response to steady-state sinusoidal inputs.

5. The closed-loop transfer function of the open-loop transfer function, G(s) = ks(1 + sT )

of a unity feedback system is

A. ks2T + s + k

B. ks(1 + sT )

C.k(1 + sT )

s

D. None of these

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Solution: Assuming that the system has a negative feedback, the transfer functionis given by

T (s) =G(s)

1 + G(s)H(s)

=

k

s(1 + sT )

1 +k

s(1 + sT )

=k

s(1 + sT ) + k=

k

s2 T + s + k

6. A unity feedback system has an open-loop gain G(s) = 10s(s + 10)

. The system has a

steady state velocity error of

A. 1

B. 2

C. 0

D. None of these

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