Oscillations of the process described by the telegraph equation for a system consisting of two segments with different densities and elasticities

A study was conducted to demonstrate oscillations of the process described by the telegraph equation for a system consisting of two segments with different densities and elasticities. Boundary conditions of the first and the second kind, one of which was allowed to be homogeneous, were considered for the investigations. Studying the longitudinal oscillations with dissipation for such a rod, which are excited at the ends x = 0 and x = l by either displacements or elastic forces and last during a time interval 0 ≤ t ≤ T, reduced to finding a solution u(x, t) of the mixed problem for the discontinuous telegraph equation on the rectangle.