A locomotive car of mass 2000 Kg traveling at a velocity v=10m/sec is stopped at the end of tracks by a spring-damper system as shown in the figure. If the stiffness of the spring is K=40 N/mm and the damping constant is c = 2 N-s/mm, determine:
a) the maximum displacement of the car after engaging the spring and damper
b) the time taken to reach the maximum displacement.