Boundary control in critical time by elastic forces applied at two ends of an inhomogeneous rod for the case in which the wave propagation time over each of the inhomogeneity parts is the same

We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the boundary control by elastic forces bringing the originally quiescent stick into a given terminal state specified by a given terminal displacement and a given terminal velocity in a given critical time.