Mechanical Vibrations (ME-502) - Important Questions

Determine the natural frequency of the undamped single-degree-of-freedom multi-spring mass system shown in Fig.2. Assume stiffness values k1 = 1 N/m, k2 = 2 N/m, k3 = 1 N/m, k4 = 4 N/m, k5 = 6 N/m.

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 and evaluate the coefficients of the Fourier series.

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

Explain what is meant by under damping, over damping and critical damping with reference to damping ratio and logarithmic decrement.

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

A heavy machine weighing 3000 N is supported on a resilient foundation. The static deflection is 7.5 cm. The machine vibrates with an amplitude under base harmonic excitation. Find the natural frequency, transmitted amplitude, transmissibility and dynamic load on the foundation.

Define magnification factor and derive its expression for a spring-mass-damper system under sinusoidal harmonic force F = F0 sin omega t.

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

Find the natural frequencies and mode shapes (amplitude ratios) for the 2-DOF spring-mass system shown in Fig.3 with k1 = 20 N/m, k2 = 10 N/m, m1 = 20 kg and m2 = 7 kg.

Determine the natural frequency of torsional vibration of a shaft with two circular discs of uniform thickness at the ends. Given masses, outer diameters, shaft length, diameter and shear modulus G.

Write short notes on relationship between sound pressure level (SPL), sound power level and sound intensity scale, including reference values and decibel calculation.