A vertical spring with constant k = 5 N/m and damping constant β = 6 kg/s has one end fixed to a wall, and a mass of 98 kg at the other end. Being in the position of equilibrium, the mass is propelled downward with a speed of 4 m/s. Suppose that on the system an external force acts in newtons given by f(t) = 8e^ −t What is the diferential equation and conditions that allow to find the position of the spring as function of a time t, with t in seconds

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