Discuss the normal modes of this system as well as a linear

Question

If K₁ = 0 in the torsional system of Problem, the system becomes a degenerate two-DOF system with only one natural frequency.

Discuss the normal modes of this system as well as a linear spring-mass system equivalent to it.

Show that the system can be treated as one of a single DOF by using the coordinate ? = (θ₁ - θ₂),

Problem

Determine the normal modes of the torsion al system shown in Fig. P5-5 for K₁ = K₂ and J₁ = 2j₂ .