Exercise 3.2. This problem is challenging! Two identical particles of mass m are connected by a light spring with stiffness k (neglect the spring’s mass) and equilibrium length 2. Ev- erything is lined up on the z-axis. Let the position of particle 1 be r(t) and the position of particle 2 be f(t). If at time t = 0, the positions are (0) = ? and r2(0) = l, and the velocities are non-zero with vi(0) = v1 +0 and v2(0) = 12 +0, determine the following: (a) The formulas describing the center-of-mass (COM) position X(t) and velocity V(t) as functions of time and the initial velocities vy, 02 and l.