Waves and Oscillations

Week 1: Oscillations in physical systems, Time period and frequency, Harmonic oscillator in one-dimension and itssolutions, Superposition of simple harmonic oscillations, Lissajous figures.Week 2: Damped harmonic oscillations and its solutions. Driven and damped oscillator and its solutions. Applicationsto vibration isolation.Week 3: Impedance, Displacement and velocity resonance, Q-factor of the oscillator.Week 4: Coupled oscillations, Normal modes and frequencies.Week 5: Coupled oscillations of loaded string, Solvable examples of coupled oscillations.Week 6: Wave equation and the transverse waves, Solutions of wave equation, Velocities in wave motion.Week 7: Standing waves, Reflection and transmission of waves at a boundary, Impedance matching.Week 8: Longitudinal waves, Sound waves in gases, Longitudinal waves in a solid, Application to periodic structures and earthquakes. Experimental techniques to measure speed of sound.Week 9: Fourier analysis, Wave pulses, Applications of Fourier analysis.Week 10:Waves in optical systems, Laws of reflection and refraction, Rays and wavefronts.Week 11:Interference and Diffraction, Newton's rings, Fabry-Perot Interferometer,Fraunhofer diffraction.Week 12:Introduction to nonlinear oscillations, Waves and solitons.