Engineering Questions with Answers - Multiple Choice Questions

Home » MCQs » Aeronautical Engineering » Machine Dynamics MCQ – Natural Frequency of Free Transverse Vibrations

# Machine Dynamics MCQ – Natural Frequency of Free Transverse Vibrations

A cantilever shaft having 50 mm diameter and a length of 300 mm has a disc of mass 100 kg at its free end. The Young’s modulus for the shaft material is 200 GN/m^{2}. Determine the frequency of transverse vibrations of the shaft.

a) 31

b) 35

c) 37

d) 41

**
View Answer**

Answer: d

Explanation: We know that deflection is given by the relation:

Wl^{3}/3E.I

I = 0.3×10^{-6} m^{4}

d = 0.147×10^{-3}

f = 0.4985/d−−√

Thus f = 41 Hz.

For the same dimensions of a beam, transverse vibrations have a lower frequency than longitudinal frequency.

a) True

b) False

**
View Answer**

Answer: a

Explanation: Keeping the dimensions of the testing beam same, it is noted that the natural frequency of vibrations obtained in longitudinal waves is larger than the one obtained in transverse waves.

A cantilever shaft having 50 mm diameter and a length of 300 mm has a disc of mass 100 kg at its free end. The Young’s modulus for the shaft material is 200 GN/m^{3}. Determine the static deflection of the shaft in mm.

a) 0.147

b) 0.213

c) 0.132

d) 0.112

**
View Answer**

Answer: a

Explanation: We know that deflection is given by the relation:

Wl^{3}/3E.I

W = 100xg, l=0.3m, I = I = 0.3×10^{-6} m^{4}

substituting values we get d = 0.147mm.

For the same dimensions of the shaft which of the following has the greater natural frequency?

a) Transverse

b) Longitudinal

c) Depends on thickness

d) Depends upon length

**
View Answer**

Answer: b

Explanation: If the dimensions of the testing beam are kept same, it is observed that the natural frequency of vibrations obtained in longitudinal waves is larger than the one obtained in transverse waves.

Calculate the natural frequency of transverse vibrations if the static deflection is 0.01mm.

a) 157.6

b) 144.8

c) 173.2

d) 154.1

**
View Answer**

Answer: a

Explanation: We know that the natural Frequency of Free Transverse Vibration is given by the equation

f = 0.4985/s√

where s is the displacement of the spring.

substituting the given values we get

f=157.6 Hz

Increasing mass will result in lower frequency.

a) True

b) False

**
View Answer**

Answer: a

Explanation: We know that deflection is given by the relation :

Wl^{3}/3E.I

Increasing the mass will result in an increased deflection which, frequency decreases as the deflection increases hence increasing mass will reduce the frequency of vibration.

Calculate the static deflection in µm of transverse vibrations if the frequency is 200Hz.

a) 6

b) 0.6

c) 60

d) 0.006

**
View Answer**

Answer: a

Explanation: We know that the natural Frequency of Free Transverse Vibration is given by the equation

f = 0.4985/s√

where s is the displacement of the spring.

substituting the given values we get

f = 0.00000621255625 m.