The two masses are connected by an inextensible cable which passes securely over the periphery of the cylindrical pulley of mass m₃, radius r, and radius of gyration k_O. Determine the equation of motion for the system in terms of the variable x. State the critical driving frequency w_c of the block B which will result in excessively large oscillations of the assembly. Evaluate for m₁ = 25 kg, m₂ = 10 kg, m₃ = 15 kg, k₁ = 450 N /m, k₂ = 300 N/m, r = 300 mm, and k_O = 200 mm.

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XB = b sin ot www B m1 M3, ko, B C m2 k2