The suspension system of a car is modelled as having an effective stiffness of 5x10⁶ (N/m) and an effective mass of 750 (kg). The car is travelling over a road with bumps that can be modeled as periodic half-sine waves as shown above. Use the first 4 terms of a Fourier series to represent the road's contour

[1] For road bumps with a height of 10 (cm) that are spaced with a period of 5 (secs) find the response of the car for 20 (secs) of travel; i.e. plot x (t) for 0 < t < 20 (secs).

[2] Design a viscous damper to add to the suspension; in parallel with the spring. For road bumps with a height of 10 (cm) that are spaced with a period of 5 (secs) find the response of the car with your suspension design for 20 (secs) of travel over the same road conditions as in [1].