Course Details
Subject {L-T-P / C} : PH2001 : Waves and Oscillations { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Prakash Nath Vishwakarma
Syllabus
Module 1: 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: 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: Coupled Oscillations and Normal Modes: Two coupled pendulums, Symmetry Consideration, Superposition of normal modes, Forced vibration and resonance for two coupled oscillatiors, Many Coupled Oscillators, Normal Modes for N coupled Oscillators.
Module 4: 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: Wave Motion: Normal modes and travelling waves, Progressive waves in one directions, 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, Polarization, Interference, Diffraction, Doppler effect.
Course Objectives
- To learn various mathematical properties of free, damped and forced oscillations in various contexts.
- To learn independent and coupled oscillation processes for various physical systems.
- To learn the use of Fourier treatment in waves and oscillations
- To learn the wave motion and energy transmission
Course Outcomes
CO1: Recognize and use mathematical oscillator equation and wave equation, and derive these equations for certain systems. <br />CO2: Understand the effect of damping and periodic force on the oscillating body. <br />CO3: Study of Lissajous figures and the motion of coupled oscillators, <br />CO4: Use of Fourier analysis in the field of oscillations and wave. <br />CO5: Use the principles of wave motion and superposition to explain the physics of polarization, interference and diffraction.
Essential Reading
- A. P. French, Vibrations and Waves, CBS Pub. & Dist , 1987
- Ajoy Ghatak, Soo-Jin Chua and I. C. Goyal, Mathematical Physics: Differential Equations & Transform Theory, Macmillan Publishers India , 2000
Supplementary Reading
- Franks Crawford, Waves: Berkeley Physics Course, Tata McGrawHill , 2007
- H. J. Pain, The Physics Of Vibrations And Waves, John Wiley & Sons , 6th Edition