# Machine Dynamics Questions and Answers – Vibratory Motion

This set of Machine Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Vibratory Motion”.

1. When there is a reduction in amplitude over every cycle of vibration, then the body is said to have
a) free vibration
b) forced vibration
c) damped vibration
d) none of the mentioned

Explanation: When no external force acts on the body, after giving it an initial displacement, then the body is said to be under free or natural vibrations. The frequency of the free vibrations is called free or natural frequency.
When there is a reduction in amplitude over every cycle of vibration, the motion is said to be damped vibration.

2. Longitudinal vibrations are said to occur when the particles of a body moves
a) perpendicular to its axis
b) parallel to its axis
c) in a circle about its axis
d) none of the mentioned

Explanation: When the particles of the shaft or disc moves parallel to the axis of the shaft, then the vibrations are known as longitudinal vibrations.
When the particles of the shaft or disc move approximately perpendicular to the axis of the shaft, then the vibrations are known as transverse vibrations.

3. When a body is subjected to transverse vibrations, the stress induced in a body will be
a) shear stress
b) tensile stress
c) compressive stress
d) none of the mentioned

Explanation: In transverse vibrations,the shaft is straight and bent alternately and bending stresses are induced in the shaft.

4. The natural frequency (in Hz) of free longitudinal vibrations is equal to
a) 1/2π√s/m
b) 1/2π√g/δ
c) 0.4985/δ
d) all of the mentioned

Explanation: Natural Frequency, fn = 0.4985/δ
where m = Mass of the body in kg,
s = Stiffness of the body in N/m, and
δ = Static deflection of the body in metres.

5. The factor which affects the critical speed of a shaft is
a) diameter of the disc
b) span of the shaft
c) eccentricity
d) all of the mentioned

Explanation: To determine the critical speed of a shaft which may be subjected to point loads, uniformly distributed load or combination of both, we find the frequency of transverse vibration which is equal to critical speed of a shaft in r.p.s. The Dunkerley’s method may be used for calculating the frequency.
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6. The equation of motion for a vibrating system with viscous damping is
d2x/dt2 + c/m X dx/dt + s/m X x = 0
If the roots of this equation are real, then the system will be
a) over damped
b) under damped
c) critically damped
d) none of the mentioned

Explanation: When the roots are real, overdamping takes place.
When the roots are complex conjugate underdamping takes place.

7. In under damped vibrating system, if x1 and x2 are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to
a) x1/x2
b) log (x1/x2)
c) loge (x1/x2)
d) log (x1.x2)

Explanation: None

8. The ratio of the maximum displacement of the forced vibration to the deflection due to the static force, is known as
a) damping factor
b) damping coefficient
c) logarithmic decrement
d) magnification factor

Explanation: Magnificiant Factor is the ratio of maximum displacement of the forced vibration (xmax) to the deflection due to the static force F(xo).
Damping Factor is the ratio of amping coefficient for the actual system, and damping coefficient for the critical damped system.

9. In vibration isolation system, if ω/ωn is less than √2 , then for all values of the damping factor, the transmissibility will be
a) less than unity
b) equal to unity
c) greater than unity
d) zero
where ω = Circular frequency of the system in rad/s, and
ωn = Natural circular frequency of vibration of the system in rad/s.

Explanation: The value of ω/ωn must be greater than √2 if ε is to be less than 1 and it is the numerical value of ε , independent of any phase difference between the forces that may exist which is important.

10. In vibration isolation system, if ω/ωn > 1, then the phase difference between the transmitted force and the disturbing force is
a) 0°
b) 90°
c) 180°
d) 270°

Explanation: There is a phase difference of 180° between the transmitted force and the disturbing force.

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