Syllabus

Module 1: (7 hours)
Periodic Motion, Simple Harmonic Motion (SHM), Rotating Vector representation of SHM, Representation of SHM by complex exponential, Superposition of simple harmonic oscillations, Beats, Lissajous figures. The Free vibrations of Physical Systems.

Module 2: (7 hours)
Damped Oscillation: underdamped, overdamped, and critically damped oscillation, Forced Oscillation and Resonance: Undamped Oscillator with Harmonic force, Forced Oscillation with Damping, Transient Phenomena, and Resonance with different Examples.

Module 3: (7 hours)
Coupled Oscillations and Normal Modes: Two coupled pendulums, Symmetry Consideration, Superposition of normal modes, Forced vibration and resonance for two coupled oscillators, Many Coupled Oscillators, Normal Modes for N coupled Oscillators.

Module 4: (8 hours)
Normal modes of Continuous Systems: Free and forced harmonic vibrations of a stretched string, Longitudinal vibration of rod, The vibration of Air column, Normal modes of three-dimensional systems, Fourier analysis: Fourier series and Fourier coefficients, Fourier analysis for continuous system.

Module 5: (7 hours)
Wave Motion: Normal modes and travelling waves, Progressive waves in one direction, Waves in specific media, Wave pulses, Superposition of wave pulses, Dispersion, Phase velocity and group velocity, Transport of energy by a wave, Momentum flow and mechanical radiation pressure. Reflection and transmission of a wave.

To learn simple harmonic motion and the superposition of harmonic oscillations.

To learn the mathematical properties of free, damped, and forced oscillations in various contexts.

To learn the independent and coupled oscillation processes for various physical systems.

To learn the use of Fourier treatment in waves and oscillations.

5. To learn the wave motion and energy transmission.

At the end of the course, students will be able to:
CO1: Solve complicated mathematical problems related to oscillators and waves.

CO2: Understand the effect of damping and periodic force on the oscillating body.

CO3: Formulate the problem of coupled oscillations and solve them to obtain normal modes of oscillation.

CO4: Use of Fourier analysis in the field of oscillations and waves.

CO5: Describe wave motion, including standing, traveling, and sound waves.

A. P. French, Vibrations and Waves, CBS Publications and Distributions (1987).

F. S. Crawford, Waves: Berkeley Physics Series, McGraw Hill Education (2017).

A. Ghatak, S. Chua and I. Goyal, Mathematical Physics: Differential Equations & Transform Theory, Macmillan Publishers India (2000)

H. J. Pain, Physics of Waves and Oscillations, John Wiley & Sons Inc. , 6th Edition (2005).