On a track that follows the contour $$r = \theta$$, a bead of mass $$1 \text{ kg}$$ begins at position $$\theta = \frac{9 \pi}{2}$$. How long in seconds does it take for the bead to roll back around to a height of $$\frac{9 \pi}{2}$$? In this universe, $$g = 1 \frac{\text{m}}{\text{s}^2}$$, and there is no friction between the bead and the track.