State the mathematical relationship between the period (T) and length (L) of a simple pendulum. An oscillating simple pendulum has an angular speed of 0.5π rads-1. Calculate its period.

The angular speed ($\omega$) of the oscillating simple pendulum is given as $0.5\pi \, \text{rads}^{-1}$.
The relationship between angular speed ($\omega$) and period ($T$) is:

$$\omega = \frac{2\pi}{T}$$

$$T = \frac{2\pi}{0.5\pi \, \text{rads}^{-1}}$$ $$T = \frac{2}{0.5} \, \text{s}$$ $$T = 4 \, \text{s}$$

The period of the pendulum is $\boxed{\text{4 s}}$.