A double-decker bus shown in Figure Q2a is to be assessed for its vertical heave

response to varying road surface topography when travelling at speed. Figure Q2b

shows a simplified 2DOF heave model. The model is simplified to two lumped

masses mi and ma which represent the chassis, wheels, and suspension system,

and the main body respectively. Two vertical linear springs of stiffness k, and k2 are

shown, plus three linear dampers with coefficients C1, C2, and c3 respectively to

represent three separate sources of energy dissipation arising from the tres, shock

absorber damping, and vortex shedding from the body. The vertical displacements

of the two masses from their equilibrium position are described by variables z1 and

z2. Variable y(t) describes the vertical input displacement arising from road surface

undulations.