The relationship between the length of a pendulum and its amplitude is not directly proportional. The length of a pendulum does not affect its amplitude. Instead, it influences the period of the pendulum, which is the time it takes for the pendulum to complete one full swing or oscillation.
The period of a pendulum is determined by its length and the acceleration due to gravity. According to the formula for the period of a simple pendulum, T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Amplitude, on the other hand, refers to the maximum displacement of the pendulum from its equilibrium position as it swings back and forth. It represents the maximum angle the pendulum makes with the vertical.
In summary, the length of a pendulum affects its period, while the amplitude of the pendulum depends on the initial conditions and the amount of energy given to the pendulum at the start of its motion.