Derive the equation of motion for the system shown in terms of the displacement x. The masses are coupled through the light connecting rod ABC which pivots about the smooth bearing at point O. Neglect all friction, consider the rollers on m₂ and m₃ to be light, and assume small oscillations about the equilibrium position. State the system natural circular frequency w_n and the viscous damping ratio ζ for m₁ = 15 kg, m₂ = 12 kg, m₃ = 8 kg, k₁ = 400 N/m, k₂ = 650 N/m, k₃ = 225 N/m, c₁ = 44 N∙ s/m, c₂ = 36 N∙ s/m, c₃ = 52 N ∙ s/m, a = 1.2 m, b = 1.8 m, and c = 0.9 m.

Transcribed Image Text:

C3 k3 m3 B a m1 k1 C1 k2 m2 B C2