A heavy ring of mass moment of inertia \(1.0 \mathrm{~kg}-\mathrm{m}^{2}\) is attached at the end of a two-layered hollow shaft of length \(2 \mathrm{~m}\) (Fig. 2.100). If the two layers of the shaft are made of steel and brass, determine the natural time period of torsional vibration of the heavy ring.

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5 cm 13 cm 4 cm Two-layered hollow shaft 2 m Brass Steel FIGURE 2.100 Heavy ring at end of hollow shaft.