m/2 êr m/2 Ꮎ k ш 27 Fig. 1: 2 Balls Two particles with mass m/2 are attached by a linear spring with a spring constant k as shown in Fig. 1. Consider arbitrary the initial position and velocity of each mass on the plane. For simplicity, however, assume that the initial separation 20 is the unstretched length of the spring, and that the mass center has zero inertial velocity initially. Determine the differential equations of motion whose solution would give r(t) and (t) as functions of time and initial conditions; it is not necessary to solve these differential equations.

m/2 êr m/2 Ꮎ k ш 27 Fig. 1: 2 Balls Two particles with mass m/2 are attached by a linear spring with a spring constant k as shown in Fig. 1. Consider arbitrary the initial position and velocity of each mass on the plane. For simplicity, however, assume that the initial separation 20 is the unstretched length of the spring, and that the mass center has zero inertial velocity initially. Determine the differential equations of motion whose solution would give r(t) and (t) as functions of time and initial conditions; it is not necessary to solve these differential equations.