Undergraduate core course for Engineering Physics Bachelor of Technology Program at IIT Bombay.
Course code: PH 202
Waves & Oscillations: Simple Harmonic motion, damped SHM, critical damping, Sustaining oscillations in a damped oscillator. Driven oscillation, resonance, damped-driven oscillator and its resonance, Q-factor, Vanderpol oscillator, non-linear feedback for sustained oscillations. SHM in 2-dim, dependence on initial conditions, Lissajous figures, condition for closed orbits, SHM in 3-dim. Oscillations of two particle systems, symmetric and asymmetric modes, general solution to the problem. Driven oscillations of two particle system. Oscillations of n particle systems, normal modes, Formulation of the general problem, eigenvalues and eigenvectors of normal modes, general solution for arbitrary initial conditions. Driven oscillations. Example of a linear triatomic molecule. Longitudinal and transverse oscillations, modding out the zero frequencies. Oscillations of a chain of n atoms. Continuum limit, vibrational modes of a string of constant density.
Equation of Motion for waves, Standing waves and travelling waves in 1 dimensions. Properties of waves in two and three dimensions Harmonics, Linear superposition of harmonics, odd harmonics, construction of pulse shapes. Fourier components of a periodic pulse, Fourier analysis and Fourier coefficients. Fourier analysis of arbitrary functions, Fourier Coefficients, Properties of Fourier transform.
Electromagnetic wave description of light, waves in vacuum, plane waves, polarization (Stokes parameters), confined waves, Gaussian wave propagation, diffraction free beams, waves in isotropic media, optical response of media, Lorentz and Drude models, dispersion and absorption, wave propagation in uniaxial media, Reflection and refraction, Fresnel`s equations and their consequences. Interference, Fabry-Perot and Michelson interferometers, interference coatings, Spatial and temporal coherence, introduction to Fourier transforms, convolution theorem, Fourier transform spectroscopy, optical coherence tomography, Fraunhofer diffraction, diffraction gratings and their uses, Fabry-Perot resonator with gain, stimulated emission, lasers and holography.
Year taught (by AK): Spring, 2020-21
Class strength: 53 students
Lecture notes available here.
Projects (2021):
Due to the lockdown, classes had to be conducted online and we could not do lab demos that I had initially planned to accompany the theory.
So with the consent of students, we experimented in this course with the idea of an executable paper for the student projects. Here the students reproduce an already published peer reviewed work. Partly inspired from here.
The code for all these projects is available publicly here. A YouTube playlist where each student group explains their work is available here.