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# Machine Dynamics MCQ – Free Torsional Vibrations of a Single Rotor System

Which of the following relation is correct regarding free torsional vibrations of a single motor system?

a) Independent of modulus of rigidity

b) Independent of polar moment of inertia

c) Dependent on mass moment of inertia

d) Independent of length of shaft

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Answer: c

Explanation: The free torsional vibrations of a single motor system depends on the following factors:

Modulus of rigidity, Polar moment of inertia, mass moment of inertia and length of the shaft.

Free torsional vibrations of a single motor system increases with increase in polar moment of inertia.

a) True

b) False

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Answer: b

Explanation: The free torsional vibrations of a single motor system depends on the following factors:

√Polar moment of inertia as directly proportional to the square root of polar moment of inertia.

If the polar moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system?

a) Increases 4 times

b) Increases 2 times

c) Decreases 4 times

d) Decreases 2 times

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Answer: b

Explanation: Since the free torsional vibrations of a single motor system depend on the square root of the polar moment of inertia of the system, increasing 4 times will lead to increase in two times the initial vibration.

If the mass moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system?

a) Increases 4 times

b) Increases 2 times

c) Decreases 4 times

d) Decreases 2 times

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Answer: d

Explanation: Since the free torsional vibrations of a single motor system depend on the inverse of square root of the mass moment of inertia of the system, increasing 4 times will lead to decrease in two times the initial vibration.

Calculate the free torsional vibrations of a single motor system from the following data:

C = 8 GN/m^{2}, L=9m, I = 600 Kg-m^{2}, J = 8×10^{4} m^{4}

a) 162,132

b) 172,132

c) 182,132

d) 192,132

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Answer: b

Explanation: The free torsional vibrations of a single motor system is given by

12(C.J÷l.I)−−−−−−−−−√

Substituting the given values gives f = 172132 Hz.

If the length inertia is decreased to nine times, then what will be the effect on free torsional vibrations of a single motor system?

a) Increases 3 times

b) Increases 9 times

c) Decreases 9 times

d) Decreases 3 times

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Answer: a

Explanation: Since the free torsional vibrations of a single motor system depends on the inverse of square root of the length, decreasing 9 times will lead to increase in 3 times the initial vibration.

Calculate the Polar moment of inertia in m^{4} of a single motor system from the following data:

C = 8 GN/m^{2}, L=9m, I = 600 Kg-m^{2}, f=10 Hz

a) 0.00027

b) 0.00032

c) 0.00045

d) 0.00078

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Answer: a

Explanation: The free torsional vibrations of a single motor system is given by

12(C.J÷l.I)−−−−−−−−−√

Substituting the given values gives J = 0.00027 m^{4}.

If radius of gyration increases then the torsional free vibration increases.

a) True

b) False

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Answer: b

Explanation: Increase in the radius of gyration will result in increase in mass moment of inertia since mass moment of inertia is not directly dependent, the given statement is false.