Reflections of waves in infinite strings due to mass-spring-damper attachments

In this paper, it is analysed how an infinite cable behaves when a wave from the right hits a TMD system attached to it. The TMD system consists of a mass M1, a spring with stiffness K, a damper with coefficient C and a second mass M2. The cable has a tension T. Then it is investigated what happens when a wave goes through the cable and hits this TMD system. The goal of this paper is to calculatehow effective this TMD system damps. Using the multiple time scale perturbation method, the displacements of the cable and TMD system are calculated. This results in the reflected wave being damped by the TMD system, but the transmitted wave having a larger is placement than expected. The displacement of the TMD system also had unrealistic outcomes. To calculate the effectiveness of the TMD system, the energy which has been lost has to be calculated. Since the displacement of the TMD system had unrealistic outcomes, the calculation ofthe energy is not realistic either.Applied Mathematic