Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts

In the present paper, we consider a boundary control by displacements at one endpoint of an inhomogeneous rod that has two parts of different densities and elasticities with fixed other endpoint for the case in which the times of passage of the wave through each of these inhomogeneity parts coincide. We find a closed analytic form of the boundary control by displacements bringing the stick from the original rest state into a given terminal state specified by given terminal displacement and velocity.