The center of the thin disk of Figure P3.48 is displaced a distance \(\delta\) and the disk released. The coefficient of friction between the disk and the surface is \(\mu\). The initial displacement is sufficient to cause the disk to roll and slip.

(a) Derive the differential equation governing the motion when the disk rolls and slips.

(b) When the displacement of the mass center from equilibrium becomes small enough, the disk rolls without slip. At what displacement does this occur?

(c) Derive the differential equation governing the motion when the disk rolls without slip.

(d) What is the change in amplitude per cycle of motion?

Transcribed Image Text:

k Thin disk of mass m ww FIGURE P3.48