A particle with a mass of .500 kg is attached to a spring with a force constant of 50.0 N/m. At time t=0 the particle has its maximum spreed of 20.0 m/s and is moving to the left. (a) Determine the particle's equation of motion, specifying its position as a function of time. (b) Where in the motion is the potential energy three time the kinetic energy? (c) Find the minimum time interval required for the particle to move from x=0 to x=1m.