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# Machine Dynamics MCQ – Types of Vibratory Motion and Natural Frequency of Free Longitudinal Vibrations

In vibration isolation system, if ω/ω_{n}, then the phase difference between the transmitted force and the disturbing force is

a) 0°

b) 90°

c) 180°

d) 270°

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Answer: c

Explanation: In Vibration-isolation system, If the phase difference between transmitted force and the disturbing force is 180°C, then ω/ω_{n} = 1.

When a body is subjected to transverse vibrations, the stress induced in a body will be

a) shear stress

b) bending stress

c) tensile stress

d) compressive stress

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Answer: b

Explanation: The critical speed of a shaft with a disc supported in between is equal to the natural frequency of the system in transverse vibrations and the stress induced is bending stress.

The critical speed of a shaft with a disc supported in between is equal to the natural frequency of the system in

a) transverse vibrations

b) torsional vibrations

c) longitudinal vibrations

d) none of the mentioned

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Answer: a

Explanation: The critical speed of a shaft with a disc supported in between is equal to the natural frequency of the system in transverse vibrations and the stress induced is bending stress.

In steady state forced vibrations, the amplitude of vibrations at resonance is _____________ damping coefficient.

a) equal to

b) directly proportional to

c) inversely proportional to

d) independent of

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Answer: c

Explanation: Forced vibration is when a time-varying disturbance (load, displacement or velocity) is applied to a mechanical system. The disturbance can be a periodic and steady-state input, a transient input, or a random input. The periodic input can be a harmonic or a non-harmonic disturbance.

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) under damped vibration

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Answer: c

Explanation: The vibrations of a body whose amplitude goes on reducing over every cycle of vibrations are known as damped vibrations. This is due to the fact that a certain amount of energy possessed by the vibrating body is always dissipated in overcoming frictional resistance to the motion.In these vibrations, the amplitude of the vibrations decreases exponentially due to damping forces like frictional force, viscous force, hysteresis etc.

In vibration isolation system, if ω/ω_{n} < 2, then for all values of damping factor, the transmissibility will be

a) less than unity

b) equal to unity

c) greater than unity

d) zero

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Answer: c

Explanation: For underdamped systems the maximum amplitude of excitation has a definite value and it occurs at a frequency ω/ω_{n}1. For damping factor, the transmissibility will be greater than unity.

The accelerometer is used as a transducer to measure earthquake in Richter scale. Its design is based on the principle that

a) its natural frequency is very low in comparison to the frequency of vibration

b) its natural frequency is very high in comparison to the frequency of vibration

c) its natural frequency is equal to the frequency of vibration

d) measurement of vibratory motion is without any reference point

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Answer: c

Explanation: Natural frequency need to be equal to frequency of vibration so that resonance exists and it should show the indication of earthquake.

While calculating the natural frequency of a spring-mass system, the effect of the mass of the spring is accounted for by adding X times its value to the mass, where X is

a) 1/2

b) 1/3

c) 1/4

d) 3/4

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Answer: b

Explanation: Velocity at a distance “y” from fixed End = Velocity at free end /length of spring x y

∆k = 1/2 x M/3 x v^{2}.

Critical speed is expressed as

a) rotation of shaft in degrees

b) rotation of shaft in radians

c) rotation of shaft in minutes

d) natural frequency of the shaft

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Answer: d

Explanation: Critical speed is expressed as natural frequency of the shaft.

The first critical speed of an automobile running on a sinusoidal road is calculated by (modeling it as a single degree of freedom system)

a) Resonance

b) Approximation

c) Superposition

d) Rayleigh quotient

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Answer: a

Explanation: Frequency of automobile and road are same.

The natural frequency of a spring-mass system on earth is ω_{n}. The natural frequency of this system on the moon (g_{moon} = g_{earth}/6) is

a) ω_{n}

b) 0.408ω_{n}

c) 0.204ω_{n}

d) 0.167ω_{n}

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Answer: a

Explanation: We know natural frequency of a spring mass system is,

ω_{n} = √k/m ………..(i)

This equation (i) does not depend on the g and weight (W = mg)

So, the natural frequency of a spring mass system is unchanged on the moon.

Hence, it will remain ω_{n} , i.e. ω_{moon} = ω_{n}.

A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d ) and damped natural frequency (f_{n}), respectively, are

a) 0.471 and 1.19 Hz

b) 0.471 and 7.48 Hz

c) 0.666 and 1.35 Hz

d) 0.666 and 8.50 Hz

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Answer: a

Explanation: Given k = 3.6 kN/m, c = 400 Ns/m, m = 50 kg

We know that, Natural Frequency

ω_{n} = √k/m = 8.485 rad/ sec

And damping factor is given by,

d = c/c_{c} = c/2√km = 0.471

Damping Natural frequency,

ω_{d} = √1 – d^{2} ω_{n}

2пf_{d} = √1 – d^{2} ω_{n}

f_{d} = 1.19 Hz.

For an under damped harmonic oscillator, resonance

a) occurs when excitation frequency is greater than undamped natural frequency

b) occurs when excitation frequency is less than undamped natural frequency

c) occurs when excitation frequency is equal to undamped natural frequency

d) never occurs

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Answer: c

Explanation: For an under damped harmonic oscillator resonance occurs when excitation

frequency is equal to the undamped natural frequency

ω_{d} = ω_{n}.