Figure 4.5.5a shows a system with two inertia elements and two torsional dampers. The left-hand end of the shaft is twisted by the angular displacement φ, which is a specified function of time. The...

Figure 4.5.5a shows a system with two inertia elements and two torsional dampers. The left-hand end of the shaft is twisted by the angular displacement φ, which is a specified function of time. The shaft has a torsional spring constant k_T
and negligible inertia. The equilibrium position corresponds to φ = θ₁
= θ₂
= 0. Derive the equations of motion.

Figure 4.5.5a