6-6. A vehicle towing a trailer through a spring-damper coupling hitch is shown in Fig. 6P-6. The following parameters and variables are defined: M is the mass of the trailer; Kh, the spring constant of the hitch; B, the viscous damping coefficient of the hitch; Bt, the viscous- friction coefficient of the trailer; y₁(t), the displacement of the towing vehicle; y2(t), the displacement of the trailer; and f(t), the force of the towing vehicle. (a) Write the differential equation of the system. (b) Write the state equations by defining the following state variables: x₁(t) = y₁(t) - y2(t) and x2(t) = dy₂(t)dt. fit),y,(t) y2(1) Kit Bit Figure 6P-6 TRAILER M B₁