The vehicle suspension system is shown below with the following parameters: m = 200 kg, k = 2500 N/m and c = 500 N.s/m. The spring is compressed 0.1 m when the tire hits the bump which gives the initial velocity 1.2 m/sec. 

Assuming the tire remains out of contact with the road after the bump the

(a) determine the damping ratio, 

(b) determine and plot the tire displacement response x(t), and, 

(c) determine the value of maximum displacement and at what time it happens.

Cars forward motion Vehice Tread contact point Road surtace Reference Mght