Machine Dynamics Multiple Choice Questions 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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
Answer: d
Clarification: 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
Answer: d
Clarification: 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.
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
Answer: a
Clarification: 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)
Answer: b
Clarification: 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