A railroad car of mass 2000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring damper system. If the stiffness of the spring is k = 80 N/mm and the damping constant is c = 20 N-s/mm determine:
a) the maximum diplacement of the car after engaging the springs and damper
b) the time taken to reach max displacement.