Geodesic
About the string with beads
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 301-306 
A. D. Myshkis; A. M. Filimonov. About the string with beads. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 301-306. http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a2/
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     title = {About the string with beads},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a classical problem of free oscillations of the 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.