The time period of a simple pendulum is the time it takes for the pendulum to complete one full oscillation or swing back and forth. The time period is primarily dependent on the length of the pendulum and the acceleration due to gravity. However, the change in amplitude of the pendulum's swing does not directly affect the time period.
For a small change in amplitude, the time period of a simple pendulum can be approximated using the small-angle approximation, which assumes that the angle of displacement is small. In this case, the time period can be calculated using the formula:
T = 2π√(L/g),
where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
To reiterate, the time period formula does not include the amplitude of the pendulum's swing. The amplitude affects the maximum displacement of the pendulum from its equilibrium position but does not influence the time it takes for the pendulum to complete one oscillation.