A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end

The present work is devoted to the construction and the rigorous justification of the solution of a boundary value problem of the longitudinal impact on a homogeneous elastic rod of a constant cross-section in the case when one of its ends is rigidly fixed, and the other end has a linear elastic element at the end and was subjected to the impact by some load.