Geodesic
Small transversal vibrations of elastic rod with point mass at one end subject to viscous friction
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 375-385

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A spectral problem describing small transversal vibrations of an elastic rod with a concentrated mass (bead) at the right end subject to viscous friction is considered. The left end is hinge-jointed. The location of the spectrum of this problem is described and the asymptotic formula of the eigenvalues is obtained. 
@article{JMAG_2009_5_a3,
     author = {I. V. Gorokhova},
     title = {Small transversal vibrations of elastic rod with point mass at one end subject to viscous friction},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {375--385},
     publisher = {mathdoc},
     volume = {5},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2009_5_a3/}
}
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I. V. Gorokhova. Small transversal vibrations of elastic rod with point mass at one end subject to viscous friction. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 375-385. http://geodesic.mathdoc.fr/item/JMAG_2009_5_a3/