A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Figure P2.38. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. How long will it take until the motion decays to a swing of only 10 degrees? Assume that the thin wire has a rotational spring constant of 2 × 10-4N m/rad and that the viscous friction coefficient for the sphere in air is 2 × 10-4 N ms/rad. The sphere has a mass of 1 kg.

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0.5 m FIGURE P2.38 Winding oscillato