Figure 1 is a graphic depiction for the heave and pitch vibration of a vehicle. The vehicle is modelled as a rigid and uniform solid rod of length L mass m and moment of inertia . The rear and front suspensions have the same sti9ness k. Establish the equations of motion for the heave and pitch (being the displacement of the centre of the mass and angular displacement about the centre of the mass, respectively). Additionally, find the natural frequencies and corresponding modes (in terms of the ratios of x1 and x2). Finally, supply a realistic scenario where this simplified model would be an appropriate starting point. How could the realism of this model be increased, and what complexity would this introduce to the analysis