A \(5000 \mathrm{~N} \cdot \mathrm{m}\) torque is statically applied to a the midspan of a solid \(20-\mathrm{cm}\) radius steel shaft \(\left(G=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}, ho=7500 \mathrm{~kg} / \mathrm{m}^{3}\right)\) with a length of \(1.5 \mathrm{~m}\) that is fixed at one end and free at its other end. The torque is suddenly removed, and torsional oscillations begin. Determine an expression for the time-dependent angular displacement of the free end of the shaft.