The lateral response of vertically translating media with variable length and tension, subjected to general initial conditions and external excitation, are determined. The translating media are modeled as a taut string and tensioned beams with pinned and fixed boundaries. In each model a rigid body is attached to the lower end of the medium and has a prescribed displacement along the horizontal direction. The rate of change of the energy of the translating medium is analyzed from the control volume and system viewpoints. The models are used to predict the forced response of a moving cable in a high-speed elevator. Three spatial discretization schemes are used to calculate the response and shown to yield the same results. The convergence of the solution for each model is investigated. The approximate solution for the string model with constant tension is compared with its exact solution from the wave method.

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