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# Machine Dynamics MCQ – Damping Factor & Magnification Factor

The ratio of the actual damping coefficient (c) to the critical damping coefficient (cc ) is known as _________

a) Damping factor

b) Damping coefficient

c) Resistive factor

d) Resistive coefficient

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Answer: a

Explanation: The ratio of the actual damping coefficient (c) to the critical damping coefficient (cc) is known as damping factor or damping ratio given by c/Cc.

Calculate critical damping coefficient in Ns/m from the following data.

mass = 200Kg

ω = 20rad/s

a) 25,132

b) 26,132

c) 27,132

d) Not possible

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Answer: d

Explanation: We know that critical damping coefficient is given by the relation

Cc = 2πxmxω

inserting the values we get

Cc = 25132 N/m/s

The above value is in N/m/s and damping factor cannot be calculated in Ns/m.

Calculate critical damping coefficient in N/m/s from the following data:

mass = 100Kg

ω = 40rad/s

a) 25,132

b) 26,132

c) 27,132

d) 28,132

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Answer: a

Explanation: We know that critical damping coefficient is given by the relation

Cc = 2πxmxω

inserting the values we get

Cc = 25132 N/m/s.

Calculate critical damping coefficient in N/m/s from the following data:

mass = 100Kg

ω = 10rad/s

a) 5,132

b) 6,283

c) 7,132

d) 8,132

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Answer: a

Explanation: We know that critical damping coefficient is given by the relation

Cc = 2πxmxω

inserting the values we get

Cc = 6283 N/m/s.

Calculate damping ratio from the following data:

mass = 200Kg

ω = 20rad/s

damping coefficient = 800 N/m/s

a) 0.03

b) 0.04

c) 0.05

d) 0.06

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Answer: a

Explanation: We know that critical damping coefficient is given by the relation

Cc = 2πxmxω

inserting the values we get

Cc = 25132 N/m/s

ratio = 800/25132.

Calculate damping ratio from the following data:

mass = 200Kg

ω = 20rad/s

damping coefficient = 1000 N/m/s

a) 0.03

b) 0.04

c) 0.05

d) 0.06

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Answer: b

Explanation: We know that critical damping coefficient is given by the relation:

Cc = 2πxmxω

inserting the values we get

Cc = 25132 N/m/s

ratio = 1000/25132 = 0.04.

Unit of damping factor is N/m/s.

a) True

b) False

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Answer: b

Explanation: Damping factor is a ratio of damping coefficient to the critical damping coefficient hence, it has no unit and is a dimensionless quantity.

Magnification factor is the ratio of the maximum displacement due to forced vibrations to the deflection due to _______

a) Static force

b) Dynamic force

c) Torsion

d) Compression

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Answer: a

Explanation: Magnification factor or the Dynamic magnifier is the ratio of maximum displacement of the forced vibration to the deflection due to the static force.

Maximum displacement due to forced vibration is dependent on deflection due to static force.

a) True

b) False

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Answer: a

Explanation: Maximum displacement due to forced vibration is directly proportional to the displacement due to static force, hence it is dependent on deflection due to static force.

In which of the cases the factor c = 0?

a) When there is damping

b) No damping

c) Resonance

d) c is never 0

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Answer: b

Explanation: When there is no damping, the factor c becomes 0 and magnification factor becomes independent of the damping coefficient.

A body of mass 20 kg is suspended from a spring which deflects 20mm under this load. Calculate the frequency of free vibrations in Hz.

a) 3.5

b) 5

c) 6

d) 7

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Answer: a

Explanation: Frequency of free vibrations is given by (1/2π)√(g/d)

substituting the value, we get

f = 3.5 Hz.

If the mass increases, then the frequency of the free vibrations increases.

a) True

b) False

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Answer: b

Explanation: Frequency of free vibrations is given by (1/2π)√(g/d), from the given formula it is evident that it is independent of mass, Hence the given statement is false.