How did the oscillation of the torsion balance allow Cavendish to calculate gravitational attraction?

In his 1798 experiment, Henry Cavendish utilized a torsion balance to measure the incredibly weak gravitational force between lead spheres.12

The apparatus consisted of a wooden rod suspended by a thin wire, with small lead spheres attached to each end. When larger stationary lead spheres were placed near them, the gravitational attraction drew the rod aside. This movement was counteracted by the restoring force of the wire’s twist, causing the rod to oscillate like a horizontal pendulum.1

By observing the balance with a telescope, Cavendish measured the period of this oscillation and the distance the rod moved. Because the gravitational force was balanced against the known restoring force of the wire, Cavendish could calculate the tiny attractive force between the masses. He then used this measurement to determine the mean density of the Earth. While Cavendish originally aimed to measure Earth's density, his precise methodology later allowed scientists to calculate the gravitational constant, G.123