Two trolleys with mass m and m2 move along a smooth surface under free-vibrational motion and constrained by three springs with stiffness coefficients k, k2 and k3 and by three dampers with damping constants C, C2 and C3. X, f1(1) k www m1 k C2 X2, f2(1) m2 k3 C3 Figure A2.1 a) Determine the governing differential equations of motion for the two masses, mi and m. [09 marks] b) If the masses m and m2 adhere to a harmonic motion with the same frequency , and two different amplitudes of a and a2 for m and m2 respectively, rearrange the differential equations in part (a). [06 marks] [04 marks] c) Determine the 'a/a' ratio in terms of M and M separately. d) Determine the frequency equation' for the said motion in terms of c. [06 marks]