Physics of Oscillators

The oscillator is an essential concept in physics: matter is often modeled as a collection of oscillators (harmonic or otherwise) interacting with each other and with the external environment. The latter acts on matter via a wave, such as an acoustic or electromagnetic wave. This allows us to lay the theoretical foundations for problems of radiation-matter interaction and thus to construct one of the fundamental tools for the study of matter (in the broad sense): spectroscopy.

Spectroscopy is the basic tool for studying the physical properties of the objects around us, such as molecules, crystals, stars, and galaxies. These properties are deduced either from their spontaneous emission or from their response to external excitation. For example, we measure the absorption, reflection, and transmission properties of applied electromagnetic radiation (visible, infrared, X-rays, neutrons, etc.). The response to this radiation is then a means of discovering the various types of oscillators that make up the medium being studied.

 In short, the study of the physical environments around us requires the use of two fundamental theoretical tools: oscillators and waves, which are precisely the subject of this course.  

The principle adopted here is a step-by-step progression from harmonic oscillators, then coupled oscillators, to waves processed within discrete systems: infinite then finite coupled oscillators with different boundary conditions.

Acquire the basic knowledge necessary to interpret certain spectroscopy experiments. Know how to perform mode calculations and construct general solutions using modal superpositions. Basic knowledge of waves and dispersion relations.

Basic Newtonian dynamics: point mechanics: elementary oscillators.  

Mastery of basic mathematics (L1): analysis and algebra.

Recommended prerequisites: In-depth knowledge of point mechanics.

CT 100%

1 - Oscillators: 
Theharmonic oscillator(definition, solution, phase space, energy).
The potential method(review, potential, nonlinear oscillations, linear limit).
Forced and damped oscillators(equation of motion, solution, power absorbed)
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2 - Coupled oscillators: Twooscillators(equations, natural frequencies, natural modes).Coupled particles(diatomic molecule, natural modes of CO2).


3 - Waves in molecular chains: Coupled particle system(potential energy, equations of motion, modes, dispersion relation, transverse and longitudinal progressive waves, band edge wave, evanescent wave). 
Finite system of coupled particles(boundary conditions, standing waves, fixed, free, and periodic ends). 
Forced end(monochromatic forcing, signal propagation, low-pass filter, resonant forcing , transmitted power, attenuation). Diatomic chain(dispersion relation, gap opening, acoustic branch and optical branch). Chain of coupled oscillators, band gap(dispersion relation, traveling and standing waves, evanescent wave, wave packet, phase and group velocities, bandwidth, Schrödinger equation, wave packet spreading).