Title | The determination of the potential q (x) in terms of natural frequencies of oscillations |
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Authors | I. M. Utyashev^{1}^{1}Mavlyutov Institute of Mechanics, Ufa Branch of the Russian Academy of Sciences |

Annotation | The 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. |

Keywords | Spectral problem, identification, potential, eigenvalues |

Citation | Utyashev 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: 12.04.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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