Chain of atoms

In the case also of a chain of masses linked by springs,  masses are attracted by their neighbors by harmonic forces (of the type -kx, k being the constant of the springs, and x its strain) . This is the classic model of a chain of atoms in a solid, and this is similar to what happens in a transmission electronic line ( the equations are of the same type ) . The number of atoms may vary here between two (which by the way is the cas of the  hydrogen molecule ) and 400 . The waves can be longitudinal or transverse . In the program are introduced only the laws of mechanics, applied to harmonic forces , and the found wave properties are only a consequence of these laws. We can thus observe the behavior of sinusoidal waves :
the positive or negative reflections , lack of reflection when the terminal mass  is submitted to a viscous force properly choosen ( characteristic impedance in case of electronic line),
the partial reflections in the case of a chain of atoms having different masses ( sonards case or echography ) ,
transmission attenuated for frequencies above the cutoff frequency ,
eigenmodes or stationary waves,
the decompositions of forced oscillation, which can be accurately observed by the graph of the total energy of the system as a function of time: there are flutterings between adjacent frequencies of the frequency imposed ; by adjusting the driving frequency and observing the graph , it is then possible to find the resonance frequencies of the chain.
the change over time of a system
initially quiet but out of equilibrium, consisting of two, three or N springs and masses.

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Publié par

Benoît Delcourt

Professeur d'Université à Paris XI, centre d'Orsay. Spécialité de recherche: la physique expérimentale des particules élémentaires. Après une thèse sur la photoproduction du méson éta, j'ai participé aux expériences sur les anneaux de collision ACO et DCI, puis sur une expérience d'annihilation p-pbar au CERN, enfin à l'epérience H1 à Hambourg. Je tiens à rendre hommage à mes maîtres, aujourd'hui disparus: Jean Pérez-Y-Jorba et Jean-Claude Bizot.