The system shown is in static equilibrium when x = 0 and x2 = 0 where x and x are the displacements of the center of mass of the uniform discs. F (t) and F (t) are forces always horizontal to the ground. Assume discs roll without slipping. The equations of motion for small oscillations about equilibrium are given in proper SI units (i.e., meters, radians, seconds, kg, N etc.) as: 1.5x200x100x = F (t) 3x2 100x+300x2= F(t) a) Using Euler-Lagrange Equations, derive the equations of motion in parametric form and determine the values of m, m2 and k ifr = 1m. For parts (b) and (c) assume F (t) = 0 and F (t) = 0. b) Calculate the natural frequencies and mode shape vectors of the system. Illustrate the mode shapes by drawing sketches for each. c) If the system is excited by such a set of initial conditions that it vibrates at the highest natural frequency only, determine x, at the instant when x = 0.01m.