Question 4.5.9: A Quarter-Car Model with Two-Masses The suspension model sho...

System Dynamics

A Quarter-Car Model with Two-Masses

The suspension model shown in Figure 4.5.9 includes the mass of the wheel-tire-axle assembly. The mass $m_{1}$ is one-fourth the mass of the car body, and $m_{2}$ is the mass of the wheel-tire-axle assembly. The spring constant $k_{1}$ represents the suspension’s elasticity, and $k_{2}$ represents the tire’s elasticity. Derive the equations of motion for $m_{1}$ and $m_{2}$ in terms of the displacements from equilibrium, $x_{1}$ and $x_{2}$ .

4.5.9

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