Consider a ball in a fixed 'U-bracket' shown below. The ball's motion is constrained by the spring (spring constant k ),

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Consider A Ball In A Fixed U Bracket Shown Below The Ball S Motion Is Constrained By The Spring Spring Constant K 1 (55.02 KiB) Viewed 15 times

The answers are:
A. one degree of freedom
B. J(theta double dot) + Kr^2 (theta) + 4Cr^2 (theta one dot) =0
Please show all steps on how to reach this solution, as muchdetail as possible would be appreciated. Will upvoteanswer.
Consider a ball in a fixed 'U-bracket' shown below. The ball's motion is constrained by the spring (spring constant k ), and the friction force (reflected by the 'translational' damping constant c ) at the point of contact with the top surface, as indicated. The bottom contact O is a no-slip point, ie., the ball rotates about O. The ball's characteristics are: moment of inertia about O is J; radius r. Assume all motions are small. a. What is the number of degrees of freedom? b. Write its equation of motion in time domain.