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QUESTION: 1

The electrical time-constant of an armature- controlled dc servomotor is

Solution:

QUESTION: 2

A mass spring system under equilibrium condition is shown in figure below.

The output displacement x(t) for M = 10 kg is given by

Solution:

The differential equation for the given system is

or,

Taking Laplace transform on both sides, we get: (10s^{2} + 30s + 20) X(s) = 1

or,

or,

QUESTION: 3

Two wheels are mechanically coupled as shown in figure below.

Here, ω_{1} and ω_{2} = angular velocities (in rad/s)

T_{1} and T_{2} = Torque (in N-m)

r_{1} and r_{2} = radius of the wheels (in cm)

θ_{1} and θ_{2} = angular displacements (in degrees)

N_{1}, and N_{2} = No. of teeths on wheels

It is given that ω_{1} = 10 rad/s, N_{1} = 40, N_{2} - 20,

T_{1} = 5 N-m, r_{1} = 20 cm and θ_{1} = 20°.

Match List-I with List-ll and select the correct answer using the codes given below the lists:

Solution:

We know that,

QUESTION: 4

The poles-and zeros of the transfer function for the mechanical system shown below are respectively

Solution:

The differential equation for the given mechanical system is

Taking Laplace transform on both sides, we get

QUESTION: 5

Consider the mechanical system shown in figure below.

Which one of the following circuits shows the force-voltage analogous electrical circuit for the mechanical diagram shown above?

Solution:

Thus, option (d) will be the correct circuit.

QUESTION: 6

Match List-I with List-II and select the correct answer using the codes given below the lists:

Solution:

For mechanical rotational system, we have:

For electrical system, we have

Comparing equations (i) and (ii), we have:

QUESTION: 7

Consider the mechanical system shown below:

The system is described by the differential equations:

Solution:

The free-body diagram for the two masses will be shown as below.

Hence, the differential equations for the two masses can be written as follows:

QUESTION: 8

Which of the following is not a desirable property of a servomotor in feedback control systems?

Solution:

Relation between electrical control system and rotor speed should be linear.

QUESTION: 9

Consider the following statements related to A.C. servomotors compared to D.C. servomotor used in control system applications.

1. It has less efficiency.

2. It is maintenance free.

3. It gives smooth operation.

4. It gives high power output.

Which of these statements is/are true regarding an A.C. servomotor?

Solution:

An A.C. servomotor doesn’t require brushes compared to a D.C. servomotor. So, it gives maintenance free operation. It’s efficiency is less due to low power output but, gives smooth operation.

QUESTION: 10

A field controlled DC servomotor is a

Solution:

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