A simplified model of a passenger car travelling over a road and vibrating in the vertical direction is shown below. The mass of the vehicle is 1000 kg, the spring stiffness of the suspension system is 500 kN/m, and there is a damping ratio of C = 0.5. (a) Determine the damping coefficient of the suspension system. (b) Determine the quality factor, Q, of the system. (c) Determine the value for when under free oscillation. (d) If the road surface is assumed to vary sinusoidally with an amplitude of 0.025 m over a length for one cycle of 6m. Determine the displacement amplitude of the vehicle if the vehicle is travelling at 30 m/s. (e) Use MATLAB to determine the damping constant required to reduce the amplitude of the vehicle to less than 10 mm. What other parameters could you change to acheive the same result?