2. (30)a. Derive the differential equations governing the two degree-of-freedom system shown, using X₁ X2 and x3 as gene
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2. (30)a. Derive the differential equations governing the two degree-of-freedom system shown, using X₁ X2 and x3 as generalized coordinates. x3 is a specified displacement input. Use Newton's method. (Data: m₁=1 kg. m2-2 kg. k₁= 100N/m k₂= 200 N/m.) b. Determine the natural frequencies and the mode shapes. c. Find the mass normalized modes shapes of the system d. Determine the steady state response (particular solution) of the system to harmonic forcing x3(t) = 0.1 Sin 10t m. Use modal analysis. X3(7) Moving base xq (1) mi X₂(1) mb