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We consider the Cauchy problem for the one-dimensional hyperbolic equation with an unknown right-hand side, which rapidly oscillates in time. This right-hand side is the product of two functions, with one being a function of a time variable and a space variable and the other one being a function of a time variable and a so-called fast time variable. We formulate and solve four asymptotic problems of exact reconstruction of the source from certain information about the partial asymptotics of the solution., Author(s): E. V. Korablina [sup.1], V. B. Levenshtam [sup.1] [sup.2] Author Affiliations: (1) https://ror.org/01tv9ph92, grid.182798.d, 0000 0001 2172 8170, Southern Federal University, , Milchakov Street, 8A, 344058, Rostov-on-Don, Russia (2) [...]