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Course: Oscilation and Waves

Department/Abbreviation: OPT/KV

Year: 2020

Guarantee: 'prof. RNDr. Tomáš Opatrný, Dr.'

Annotation: Understand basic principles of virational motion and apply them to solving problems of various physical systems. Understand principles of wave propagation in different media or fields and learn to solve corresponding model problems.

Course review:
Free undamped harmonic oscillations: oscillators in nature and industry, equations of a harmonic oscillator, energy of the oscillations, phase space, superposition of oscillations. Free oscillations with damping: examples of damped oscillations, underdamped, critically damped and overdamped motion. Forced oscillations: examples of forced oscillators, equation of forced oscillations and its solution, resonance, Q-factor of a resonator, impedance. Coupled oscillators: examples of coupled oscillators, normal modes and methods of finding their frequencies. Coupled oscillators in nature and industry, mechanical and electrical oscillators. Waves in 1D: transversal wave equation of a string and its solution, normal modes of a finite string, Fourier metod. Propagation of a disturbance on an infinite string, reflection and transmission of a wave on a boundary, wave polarization. Longitudinal waves, sound propagation in air. Interference of waves: Mach-Zehnder interferometer, Michelson interferometer. Resonators, Fabry-Perot interferometer. Superposition of waves, modulation, wave packets, pulses. Waves in 2D and 3D: wave equation, estimation of the number of modes. Solution of the wave equation af a membrane and of a 3D body. Electromagnetic waves in vacuum and in dielectric. Dispersion: nonideal string with stiffness, phase and group velocity, propagation and dispersion of wave packets. Pulses in optical fibres, chirp, slow light in media with Electromagnetically Induced Transparency. Waves in nonlinear media: higher harmonic generation, downconversion. Solitons.