A \(10,000-\mathrm{N} \cdot \mathrm{m}\) torque is applied to the midspan of the shaft of Chapter Problem 10.3 and suddenly removed. Determine the time-dependent angular displacement of the midspan of the shaft.

Data From Chapter Problem 10.3:

A steel shaft \(\left(ho=7850 \mathrm{~kg} / \mathrm{m}^{3}, G=85 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)\) with a inner radius of \(30 \mathrm{~mm}\), outer radius of \(50 \mathrm{~mm}\), and length of \(1.0 \mathrm{~m}\) is fixed at both ends.