The period of a simple pendulum is influenced by its length and the acceleration due to gravity.

The period of a simple pendulum, defined as the time required for the pendulum to complete one full oscillation (swinging back and forth), is fundamentally determined by two key factors: the length of the pendulum and the acceleration due to gravity. This relationship is mathematically represented by the formula:

Here, $T$ represents the period, $L$ denotes the length of the pendulum, and $g$ signifies the acceleration due to gravity.

The length of the pendulum is measured as the distance from the pivot point to the center of mass of the pendulum bob. A longer pendulum takes more time to complete its swing, resulting in a longer period. This occurs because a longer pendulum has to cover a greater distance with each oscillation, thereby requiring more time for each complete cycle.

The acceleration due to gravity reflects the rate at which objects are pulled towards the Earth because of gravitational force. This value is approximately $9.81 \, \text{m/s}^2$ at the Earth’s surface. When the acceleration due to gravity increases, the pendulum bob accelerates more quickly toward its equilibrium position, leading to a shorter period.

It is essential to understand that the mass of the pendulum bob does not influence the period. This phenomenon arises from the principle of equivalence, which states that all objects fall at the same rate in a gravitational field, irrespective of their mass. This principle is a fundamental aspect of Einstein’s theory of general relativity.

In practical scenarios, additional factors such as air resistance and the amplitude of the swing can impact the period of a pendulum. However, in the idealized model of a simple pendulum—where we assume negligible air resistance and small amplitude swings—the period is exclusively determined by the length of the pendulum and the acceleration due to gravity.