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 ,
damping,
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.
To download at the same time the 9 applications of Physics of the same author(atom chain)
