The assembly of Prob. 8/40 is repeated here with the additional information that body ABC now has mass m4 and a radius of gyration k_O about its pivot at O, about which it is balanced. If a harmonic torque M = M₀ cos wt is applied to body ABC, determine the equation of motion for the system in terms of the variable x. State the critical frequency c of the harmonic torque which will result in an excessively large system response. Evaluate w_c for m₁ = 15 kg, m₂ = 12 kg, m₃ = 8 kg, m₄ = 6 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, c = 0.9 m, and k_O = 0.75 m. What is the damping ratio ζ for these conditions?

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C3 k3 m3 M = Mo cos ot А a m4, ko m1 k1 C1 k2 m2 B C2