Problem 2 free torsional vibration of two rotor system, torsionally equivalent shaft

A shaft shown in diagram carries two rotors A and B. The mass of rotor A is 300 kg with radius of gyration of 0.75 m, while the mass of rotor B is 500 kg with radius of gyration of 0.9 m
1. Find the natural frequency of torsional vibration.
2. It is desired to have the node at mid section of the shaft of diameter 120 mm by changing the diameter of the portion of shaft having 90 mm diameter. What would be the new diameter?
Assume G = 84× 10^9 N/m^2

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