When a force of 1600 Newtons is applied to a spring suspended from the ceiling, it stretches 2 meters. A mass of 50 kg is connected to the end of the spring and it comes to rest at its equilibrium position. The mass is then set into motion by being pushed up from its equilibrium position with a velocity of 28 m/s. (Let the positive direction be downwards.) 1. Write the equation of motion that governs the mass-spring system described above.
2. Identify the initial conditions and solve the differential equation from part (a) with the given initial conditions.