Spring–mass chains: Theoretical and experimental studies

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Abstract
The problem of a vibrating chain of springs and masses is solved by various methods, and its density of states is obtained. The ordered chain solution is exact, and disordered cases are treated by both exact and approximate methods. Green’s function methods, iterative renormalization group calculations, concepts of statistical fluctuation and localization, as well as computational tools currently used in statistical mechanics are introduced to undergraduate students. Furthermore, the present classical system is formally the same as the tight-binding one-orbital approximation for electronic systems, and also can be used to introduce this quantum problem. Finally, the results of an experiment performed on an air track are presented and compared with their theoretical counterparts.

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