One end of a spring of constant k = 9 N/s is fixed, and a mass of m = 1 kg is attached to its other end. Initially the spring is at rest in equilibrium with zero displacement. If an external periodic force of F(1) = 80 cos5t N acts on this system, and the spring is set for vertical vibrations, described the initial value problem mathematically, and then find the subsequent displacement of the spring.
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