Figure illustrates two shafts connected at their ends by

Question

Question: Figure illustrates two shafts connected at their ends by gears. The gears are rigidly engaged. Neglect torsional drag (friction) at bearings and perform the following tasks:

(a) Select coordinates and draw the free-body diagram for each disk.

(b) Apply the kinematic constraint to eliminate the unneeded coordinate. State the separate independent equations of motion and put them in matrix format

(c) Determinethe eigenvalues and eigenvectors for the following properties: M₁ = 100 kg, r₁ = 200 mm, L₁ = 3000 mm, d₁ = 50 mm, M₂ = 50 kg, r₂ = 150 mm, M₃ = 25 kg, r₃ = 75 mm, L₂ = 1500 mm, d₂ = 75 mm, M₄ = 250 kg, r₄ = 200 mm, G₁ = G₂ = 80 GPa.