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About the string with beads. (English) Zbl 1094.74027

Summary: We consider a classical problem of free vibrations of an elastic weightless string with \(N\) beads which has been originally studied by Lagrange. We prove that for \(N\) being prime or a power of 2 the maximal displacement of the bead from its equilibrium position increases to infinity as \(N\to\infty\) while the total energy of system remains bounded by independent on \(N\) constant.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K05 Strings
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