Mechanical Vibrations (ME-502) - Important Questions

Determine the natural frequency (or required mass for a given natural frequency) of the undamped single-degree-of-freedom multi-spring mass system shown in Fig.2.

The impact force created by a forging hammer can be modeled as shown in Fig.1. Determine the Fourier series expansion of the impact force.

Find the natural frequency of the given SDOF system shown in Figure 1.

Derive / find the natural frequency of the system shown in Fig.1.

For a pump mass at midspan of a simply supported beam operating at given rpm, find the cross-sectional moment of inertia values for which oscillations are within 3 Hz of resonance.

Enlist the main causes of vibrations, and advantages and disadvantages of vibrations

Given harmonic force $F_0 \sin\omega t$ and steady-state displacement $x_0 \sin(\omega t - \phi)$, find the work done over specified time intervals (e.g., first cycle, first second, first quarter second).

Define degree of freedom of a system. Give examples of different types of degree of freedom system.

Determine the original suspended mass and spring constant from the change in natural frequency when added mass lowers the frequency from 3.56 Hz to 2.9 Hz.

Define the following terms?

Draw the FBD, derive the differential equation of motion of the vibrating system in Figure 1, and explain why viscous damping is used for modelling.

Derive the natural frequency of vibration of the system with rigid weightless bar AB.

Given mass, stiffness and viscous damping coefficient, find the critical damping and logarithmic decrement.

For a gun barrel recoil mechanism with critically damped dashpot, determine recoil parameters such as critical recoil velocity, critical damping coefficient, and required spring stiffness given mass, recoil distance and initial velocity.

Given stiffness, critical damping, logarithmic decrement and initial displacement and velocity, determine the maximum displacement of the viscously damped system.

Explain what is meant by under damping, over damping and critical damping (including damping ratio and logarithmic decrement).

For a given spring-mass-damper system, calculate critical damping constant, damping ratio, damped natural frequency, logarithmic decrement and number of cycles for amplitude reduction.

Explain why logarithmic decrement cannot be used to measure viscous damping ratios greater than or equal to one.

Derive the vibration response expression for a single degree of freedom under-damped system.

What is viscous damping? Explain the concept.

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.

Given damped natural frequency and resonant frequency for maximum amplitude under constant force excitation, find damping ratio and undamped natural frequency.

Derive the expression for frequency of free damped vibrations.

What is whirling of shaft? Derive the expression and show that the whirling critical speed equals the natural transverse vibration frequency, with physical significance.

Numerical on displacement transmissibility and vibration isolation under base/support harmonic excitation: find natural frequency, transmitted amplitude, acceleration, dynamic load, damping and isolator stiffness/deformation.

Discuss the principle of a seismic instrument (vibrometer and accelerometer) and derive its response expression with a sketch.

Find the total response of an underdamped single-degree-of-freedom system with given $m, c, k, x_0, \dot{x}_0$ under harmonic excitation and for free vibration.

Define magnification factor and derive its expression for a spring-mass-damper system under sinusoidal harmonic force $F = F_0 \sin \omega t$.

Determine the steady-state vibration amplitude of a machine with rotating unbalance given mass, excitation frequency, unbalance, stiffness and damping.

Determine the critical speed of rotation for a simply supported massless shaft with a central rotor disc.

Numerical on force transmissibility for unbalanced machine: select mounting stiffness for given transmitted force ratio and find transmitted force amplitude.

Write short notes on vibration isolation, transmissibility and magnification factor.

Define critical speed of a system.

Find the lowest natural frequency of vibration of the given beam system with specified $E$ and $I$.

Check safety of operating speed for a cantilever shaft with an overhung rotor including gyroscopic effects.

Find the natural frequencies and mode shapes (amplitude ratios) for the 2-DOF spring-mass system in Fig. 3

Determine the principal coordinates for the spring-mass system

Determine the natural frequency of torsional vibration of a shaft with two discs at the ends given disc masses, diameters, shaft dimensions and shear modulus.

Determine the natural frequencies and normal modes of a two-rotor torsional system with given stiffness and inertia ratios.

Find the natural frequency of torsional oscillations for the given system neglecting shaft inertia.

Find the natural frequency of a car given total mass, wheelbase, CG position, radius of gyration and front/rear spring stiffnesses.

Write short notes on relationship between sound pressure level and sound power level, octave band analysis, hearing conservation criteria, and viscous vs Coulomb damping

Write a short note on the decibel scale, SPL in noise, meaning of 0 dB SPL, and scale for measuring sound intensity.

Explain in brief, following terms with respect to noise:

Calculate change in sound intensity level in dB when distance from source is doubled

Calculate actual acoustic pressure from a given SPL value in air

Explain hearing conservation and damage risk criteria for normal human being.

Explain the precautions, remedies and strategies adopted for noise control of machines.

Discuss response of human to noise.

Write a short note explaining what is octave band analysis of sound

Explain sound pressure level (SPL) and sound intensity scale, including reference values, 0 dB meaning and loudness interpretation

Attempts all question in brief:

Write short notes on any two: