When a force of 960 Newtons is applied to a spring suspended from the ceiling, it stretches 2 meters. A mass of 30 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 12 m/s. (Let the positive direction be downwards.) Write the equation of motion that governs the mass-spring system described above. (Use yp for y' and ypp for y".) Identify the initial conditions and solve the differential equation from part (a) with the given initial conditions. y(t) = the general equation of a damped mass spring system is m d^2 y/dt^2 + c dy/dt + ky = 0, where m is the mass, c is the damping coefficient and k is the spring constant as determined by Hooke's Law. How does the direction in which the mass is pushed affect the initial velocity? What is the initial position of the mass in this problem