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Step 1: FBD
Draw individual free-body diagrams for the collar A and the disk. Do not forget the friction force on the disk at C when drawing your FBD of the disk. Define a coordinate x that describes the motion of the disk center O. Let's say you choose x to be positive to the left. Be sure that the directions of the spring forces on the collar are consistent with your definition of x.
Step 2: Kinetics - Newton/Euler
Write down the Newton/Euler equations for the collar and the disk. Be sure to abide by the sign conventions defined for θ and x when writing down these equations.
Step 3: Kinematics
The kinematics that you need here are to relate θ and x. Be reminded that the contact point C is the instant center for the disk. As before, be sure to abide by the sign conventions defined for θ and x. For x defined positive to the left and θ defined positive CCW, we have x = +Rθ .
Step 4: Equation of motion
Combine your equations from Steps 2 and 3 to end up with the differential equation of motion for the system.