Theory of Vibration — Summer 2025

What are the main causes of Vibration? Write down the advantages and disadvantages of vibration.

Describe the Vector method of representing harmonic motion.

Derive differential equation of motion by the energy method and Rayleigh’s method.

Define: Natural Frequency, Damping Ratio, Time Period.

Define: Damped natural frequency, Periodic motion, Amplitude, Degree of freedom.

Explain under damped, over damped and critically damped systems with graph.

Define logarithmic decrement. Also Derive the expression for logarithmic decrement.

Explain the types of vibrations in brief.

Derive the expression for frequency of free damped vibrations?

Derive solution for Spring mass damper system with harmonic force.

Explain Critical speed or Whirling speed of shaft.

What's the difference between single and double degrees of freedom?

What is vibration absorber and vibration isolator? With neat sketch explain the working of Vibration absorber. Also explain its need.

Define Transmissibility. Briefly explain the concept of support motion.

Write down the equation of motion for damped free vibration. Derive the solution for that equation.

Explain how vibration and frequency measuring devices work? Explain any one of the vibration measuring instrument in detail.

Discuss, the Principal modes of vibrations

Define: Multi degree of freedom system. Name the various methods used to analyze these systems.

Derive the solution: mx + cx + kx = Fsin ωt.

Discuss the reciprocity theorem in brief.

What is the vibration of a continuous system? Explain in brief: Vibration of strings

Derive an expression for frequency of torsional vibration of two rotor systems.

What is Resonance? How it can be avoided?

Explain in detail the Galerkin’s Method.

Write a note on Co-ordinate Coupling.