For a simple pendulum, the graph between Tz and L (where T is the time period and L is the length) is

The time period (T) of a simple pendulum is governed by the formula T = 2π√(L/g), where L is the length and g is the acceleration due to gravity. To understand the relationship between the square of the time period (T²) and the length (L), we square both sides of the equation to obtain T² = (4π²/g)L. This mathematical expression follows the linear equation form y = mx, where y represents T², x represents L, and the slope m is the constant (4π²/g). Consequently, a graph plotted with T² on the vertical axis and L on the horizontal axis results in a straight line passing through the origin. This linear relationship confirms that the square of the period is directly proportional to the pendulum's length, provided the oscillation amplitude remains small.