Final answer:
The period of a simple pendulum is determined by its length and the local acceleration due to gravity, and it is independent of the mass of the pendulum or its amplitude for small swing angles. Therefore, a pendulum can be used to measure the acceleration due to gravity accurately.
Step-by-step explanation:
The period determined with the ball in the pendulum is an important concept in physics, particularly when discussing simple harmonic motion. The key equation for a simple pendulum's period is T = 2π√(l/g), where T is the period of oscillation, l is the length of the pendulum, and g is the acceleration due to gravity. Notice that the mass of the pendulum is not a factor in calculating the period. This is because the mass does not affect the speed of the pendulum's swing within the same gravitational field.
Additionally, the period is only negligibly influenced by the amplitude of the swing if it is less than about 15°, showing that for small angles, the motion of the pendulum closely resembles simple harmonic motion. An understanding of this concept can allow for the use of a pendulum to accurately measure the acceleration due to gravity, which can vary slightly depending on location on the Earth's surface.