The single degree of freedom model of a vehicle shown below will be used to obtain a first approximation of the dynamic behavior of the entire vehicle. The mass m of the vehicle is 1200 kg when fully loaded and 400 kg when empty. The spring constant k is 400 kN/m and the damping ratio _f is 0.4 when the vehicle is fully loaded. The vehicle is traveling at 100 km/h over a road whose surface has a sinusoidally varying roughness with a spatial period of 4.0 m. We also make the following assumptions about the behavior of the vehicle: - As the vehicle moves forward at constant speed, only the vertical motion u(t) is relevant to the analysis. - The tire is infinitely stiff, i.e., z(t) represents the motion of the axle of the vehicle. - The tire remains in contact with the road.

Compute (Using Matlab) the steady-state displacement transmissibility (DT) for the vehicle when it is:

1) fully loaded, and

2) empty, and plot the DT vs. r curves for both together. Estimate the vehicle velocity at which the DT (fully loaded) would be maximum.

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