In an experiment, a 5-kg mass is suspended from a spring. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 75 cm. The mass is then displaced 36 cm upward from its spring-mass equilibrium and then given a sharp downward tap, imparting an instantaneous downward velocity of 0.45 m/s. Set up (but do not solve) the initial value problem that models this experiment. Assume no damping is present.