Response of Discrete Systems: Transient + Steady State Response

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Recall from lecture that the total response is combination of the complementary solution and the particular solution. For harmonic excitation on a single-DOF system, this total response will be composed of two frequencies: the natural frequency and the forcing frequency. With damping, the component with the natural frequency will die away ("transient" response) and that with the forcing frequency will persist ("steady state") response. The animation below shows how the two solutions combine to form the response. Can you see the two frequencies in this response?