Two trolleys with mass m and m2 move along a smooth surface under free-vibrational motion and...

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Two trolleys with mass m₁ and m2 move along a smooth surface under free-vibrational motion and constrained by three springs with stiffness coefficients k₁, k2 and k3 and by three dampers with damping constants C₁, C2 and C3. X₁, f1(1) k₁ www m1 k₂ C2 X2, f2(1) m2 k3 C3 Figure A2.1 a) Determine the governing differential equations of motion for the two masses, mi and m₂. [09 marks] b) If the masses m₁ and m2 adhere to a harmonic motion with the same frequency , and two different amplitudes of a₁ and a2 for m₁ and m2 respectively, rearrange the differential equations in part (a). [06 marks] [04 marks] c) Determine the 'a₁/a₂' ratio in terms of M₁ and M₂ separately. d) Determine the frequency equation' for the said motion in terms of c. [06 marks] Two trolleys with mass m₁ and m2 move along a smooth surface under free-vibrational motion and constrained by three springs with stiffness coefficients k₁, k2 and k3 and by three dampers with damping constants C₁, C2 and C3. X₁, f1(1) k₁ www m1 k₂ C2 X2, f2(1) m2 k3 C3 Figure A2.1 a) Determine the governing differential equations of motion for the two masses, mi and m₂. [09 marks] b) If the masses m₁ and m2 adhere to a harmonic motion with the same frequency , and two different amplitudes of a₁ and a2 for m₁ and m2 respectively, rearrange the differential equations in part (a). [06 marks] [04 marks] c) Determine the 'a₁/a₂' ratio in terms of M₁ and M₂ separately. d) Determine the frequency equation' for the said motion in terms of c. [06 marks]