k₁ m2 m₁ C₂ my Figure 1 a) Obtain the differential equation of motion of the forced vibration system shown in Figure 1 using Lagrange's equation or Newton's second law. The moment M is given by M= Mo sin(wft) 0 where Mo = 2 Nm, and w₁ = 5 rad/s. Assume small oscillations, m₁ = m2 = m3 = 1 kg, k₁ =k2=10N/m, c₁ = c2 = 10 Ns/m and 1 = 0.5m. b) If c₁ = c2 = 0, obtain the steady-state solution.