2. The schematic shows a stepped pulley (a single rigid body) that is connected to a block of mass m by an inextensible string. The pin at point O is assumed frictionless. The stepped pulley mass moment of inertia about O is J. The coordinates (t) and x(t) are relative to the system’s equilibrium state. Both are assumed k small. The mass is assumed to translate vertically, but not horizontally. It does not tilt. Derive the RA equation of motion in terms of the rotation of the pulley O(t) for the system using Newtonian mechanics. Determine expressions for the undamped natural frequency, critical damping m coefficient, and damping ratio in terms of the system’s parameters (i.e., m, ], c, k, R1, and R2). X(t) .

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