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, as shown in Figure 2. The stiffness of the spring is k = 80 N/mm and the damping constant is c = 20 N-s/mm. (a) Show that the maximum displacement of the car after engaging the springs and damper can be written as tan (wat + ) √1-52 S (Hint: the maximum displacement happens when the derivative of response with respect to time is equal to zero.) (b) What are the values for initial displacement and initial velocity for the spring-mass-damper? 1 k/2 P 0000 0000 k/2 Figure 2 (c) Find the time taken for this system to reach the maximum displacement. (d) What is the value of maximum displacement?