Acar with mass m,-1500 kg connected with a caravan of mass m2=1000 kg through a coupler as shown in figure 1 and we restrict are study to a motion only in one direction (just straight motion of the car, which is the longitudinal direction as shown in fig. 1). the coupler is considered massless in comparison with the two connected vehicles and can be modeled as a spring of stiffness of k=70,000 n/m (without any damper). fig. 1 simplified model of the above mechanical system a) identify masses, motions with the associated position and velocity variables. (20/100) b) determine the kinetic and potential energies of the system. (mark 30/100) c) use lagrange equation to derive the equations of motion, and write the equations of motion in matrix form. (mark 50/100)