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The determination of the potential q (x) in terms of natural frequencies of oscillations

TitleThe determination of the potential q (x) in terms of natural frequencies of oscillations
AuthorsI. M. Utyashev1
1Mavlyutov Institute of Mechanics, Ufa Branch of the Russian Academy of Sciences
AnnotationThe problem of determining the potential $ q (x) $ of a special type with respect to natural frequencies of oscillations is considered. In particular, we consider a potential of the form $ q (x) = q_1 + q_2 x $, which describes a linear change in the elasticity coefficient of the medium. It is shown that the coefficients $ q_1 $ and $ q_2 $ characterizing the linear change in the elasticity coefficient of the medium are uniquely determined by the three natural frequencies of the string vibrating in this medium.
KeywordsSpectral problem, identification, potential, eigenvalues
CitationUtyashev I. M. ''The determination of the potential q (x) in terms of natural frequencies of oscillations'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 348-352. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper48.pdf. - Date of access: 24.06.2019.