Deriving expression for equivalent spring constant, Physics

Deriving expression for equivalent spring constant

Assignment:

Gear A in Problem below is subjected to the torque MA = Mocoswt. Derive an expression for the angular motion of gear B.

The system shown in Fig. consists of two gears A and B mounted on uniform circular shafts of equal stiffness GJ/L; the gears are capable of rolling on each other without slip. Derive an expression for the equivalent spring constant of the system for the radii ratio R_A/R_B = n.

Provide complete and step by step solution for the question and show calculations and use formulas.

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