What is the formula for calculating the period of a pendulum?

The formula for calculating the period of a pendulum, which represents the time it takes for one complete swing back and forth, is given by ( T = 2\pi\sqrt{\frac{L}{g}} ). In this formula, ( T ) is the period, ( L ) is the length of the pendulum, and ( g ) is the acceleration due to gravity.

This formula arises from the principles of simple harmonic motion, where the period is influenced by the length of the string or rod of the pendulum and the gravitational force acting on it. As the length ( L ) increases, the period ( T ) gets longer, indicating that it takes more time to complete a full swing. Conversely, if ( g ) increases, which typically implies an increase in gravitational force (like being on a planet with stronger gravity), the period decreases, meaning the pendulum swings faster.

Other options provided do not correctly reflect the relationship between period, length, and gravity. For instance, one option misrepresents the relationship by omitting the square root and the factor of ( 2\pi ), while another suggests a direct proportionality between ( g ) and ( L ), which isn't accurate