Determine the equation if the force is suddenly moved show, Physics

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Determine the equation if the force is suddenly moved show

Assume that a lightly damped system is driven by a force F₀Sinω_ntv where ω_n is the natural frequency of the system. Determine the equation if the force is suddenly moved. Show that the amplitude decays to a value e-1 times the initial value in the time t=1/f_nδ.

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