Table of Contents

Toggle## Important** RGPV Question**

**ME-502 MECHANICAL VIBRATION**

**V Sem, ME**

**UNIT 1- **Fundamental Aspects of Vibrations

**Q.1)** What are main causes of vibrations?

**(RGPV June 2023)**

**Q.2) **A harmonic force FΒ sinΟ acts on a displacement xo sin(x-3). If Fo=100, x = 0.02 m and w=2n rad/sec.Find the work done during

**i) First cycle**

**ii) The first second**

**iii) The first quarter second**

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**Q.3) **Find the natural frequency of the car with following conditions: Total mass of car = 300 kg, wheel base 3.0 m centre of gravity of the car is 1.5 m from the front axle, radius of gyration is 1.0 m and spring constants of front and rear springs are 70×103 N/m each.

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**Q.4) **Find the natural frequency of torsional oscillations for the system shown in Fig.1. Take G=0.83Γ10ΒΉΒΉ N/mΒ² and neglect the inertia effect of the shaft.

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**Q.5) **In a spring mass vibrating system, the natural frequency of vibration is 3.56Hz. When the amount of the suspended mass is increased by 5kg, the natural frequency is lowered to 2.9 Hz. Determine the original unknown mass and the spring constant.Β

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**Q.6)Β **A system is shown in the following figure 2. The bar AB is assumed to be rigid and weightless. The natural frequency of vibration of the system is given by

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**Q.7)Β **Derive expression for two natural frequencies for small oscillations of the pendulum stain in figure 3 in the plane of the paper, assumes rods as massless and rigid Also obtain expressions for angular amplitude ratio in the two rods.

**(RGPV June 2020)**

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**Q.8)Β ** For the system shown in figure 2 below kβ = 2000 N/m, kβ = 1500 N/m, kβ = 3000 N/m, kβ = k = 500 N/m find m such that the system has a natural frequency of 10 Hz.Β Β Β Β Β **(RGPV June 2020)**

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**Q.9)Β **Derive the differential equation of the motion for a spring controlled simple pendulum shown in figurel below. The spring is in its unstretched position when the pendulum rod is vertical.Β Β

**(RGPV June 2020)**

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**Q.10)Β **Define the following terms?

i) Vector representation of the displacement, velocity, and acceleration of SHM

ii) Fundamental mode of vibration

iii) Mathematical definition of Simple Harmonic Motion (SHM)

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**Q.11) **Enlist causes of Vibration? Advantages and disadvantages of Vibrations.Β

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**Q.12)Β **A body describes simultaneously two motions:

x1= 3 sin 40 t, x2 = 4 sin 41 t.

What are the maximum and minimum amplitude of the combined motion and what is the best frequency?

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**Q.13) **Define degree of freedom of a system. Give examples of different types of degree of freedom system.

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**UNIT 2-Damped Free Vibrations & Viscous damping**

**Q.1) **What is viscous damping? Explain.

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**Q.2)** A damper offers resistance 0.05 N at constant velocity of 0.04 m/sec. The damper is used with k = 9 N/m. Determine the damping and frequency of the system when the mass of system is 0.1 kg.

**(RGPV June 2023)**

**Q.3) **The damped natural frequency of a system as obtained from a free vibration test is 10.5 Hz. During the forced vibration test with constant excitation force the maximum amplitude of vibration is found to be 9.5 Hz. Find the damping factor and it’s natural frequency.

**(RGPV June 2023)**

**Q.4)** A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m. Find the value of critical damping of the system and the value of logarithmic decrement of the vibrating system.

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**Q.5) **Why we use Viscous damping for modelling the vibrating system. Explain in brief.

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**Q.6) **Derive the expression for frequency of free damped vibrations.

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**Q.7)Β **Draw the FBD of the system and derived the differential equation governing by vibrating system is (Figure 1)Β

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## UNIT 3- Harmonically excited Vibration

**Q.1) **Define critical speed of a system.

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**Q.2)Β **Prove that the critical speed of whirling speed for a rotating shaft is same as the frequency of natural transverse vibration.

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**Q.3) **What are the principles on which a Vibrometer and an accelerometer are based? Derive the expression.

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**Q.4)Β **A right cantilever steel shaft of 0.3 m effective length has a heavy rotor fixed at its end. The mass of the rotor is 10 kg and has a radius of gyration of 12 cm about its axis. The thickness of the rotor is 6 cm. The moment of inertia of the section of the shaft about its neutral axis is 10 cmΒ². This shaft is to run at 10,000 rpm. Check if this operating speed is safe.

**(RGPV Nov 2022)**

**Q.5)Β **Determine the power required to vibrate a spring mass dashpot system with an amplitude of 1.5cm and at a frequency of 100Hz. The system has a damping factor of 0.05 and a damped natural frequency of 22 Hz as found out from the vibration record. The mass of the system is 0.5 kg.

**(RGPV June 2020)**

## UNIT 4-Systems With Two Degrees of FreedomΒ

**Q.1) **A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K = 2 kN/m. C = 500 Ns/m and the stiffness of the torsional spring kΞ is 1 kN/m/rad. Ignore the hinge dimensions.

i) Find the un-damped natural frequency of oscillations of the bar about the hinge point.

ii) The damping coefficient in the vibration equation.

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**Q.2) **Find the natural frequencies and first two normal mode shapes of the system shown in Figure 3.

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**Q.3) **Find the lowest natural frequency of vibration of system shown in Figure 4.

**(RGPV Nov 2022)**

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## UNIT 5-Noise Engineering Subjective response of sound

**Q.1)** Discuss response of human to noise.

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**Q.2)** What precautions and remedies are adopted to avoid noise of machines?

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**Q.3)Β **Write the Logical Explanation with neat sketch if needed:

i) What is SPL in noise?

ii) Does 0db SPL mean no sound pressure?

iii) How loud is 100dB SPL?

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**Q.4)Β **What is octave band analysis of sound?

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**Q.5) **Write short notes on followings.

a) Sound pressure level and sound intensity scale

b) Main sources of noise on road and in industries

c) Strategies of noise control

d) Octane Band Analysis

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**Β EXTRA QUESTION-**

**Q.1)** Write short notes on any two:

a) Energy method of solving vibration problem

b) Solid and structural damping

c) Dynamic vibration absorber

d) Measurement of noise

**(RGPV June 2023)**

**— Best of Luck for Exam —**