A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution is 9 N/m, where the damping force is negligible. At the instant t =0, the ball is 0.2 m below the equilibrium position, where it is given a downward velocity of 1 m/s. From that instant, an external force g(t) = 18 sin (t) in newtons is activated and intervenes in the system. Using the given information: Write a differential equation and conditions that describe the position of the ball at time t in seconds. Also find the position function for the ball at any time t in seconds and determine the speed of the ball when t= 1 seconds and the position at 5 seconds.

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