When measuring the acceleration due to gravity, often denoted as "g," using a pendulum or oscillatory motion, it is common to use a small amplitude. This approach is employed to ensure that the motion remains in the linear regime, where the relationship between the period and the length of the pendulum or the oscillation frequency remains constant.
The relationship between the period of a simple pendulum and its length is given by the equation:
T = 2π√(L/g)
Where: T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
In this equation, you can see that the period of the pendulum is inversely proportional to the square root of the acceleration due to gravity. By using a small amplitude, the pendulum motion remains close to the linear regime, ensuring that the period remains constant.
If a large amplitude were used, the motion of the pendulum or oscillatory system would deviate significantly from the linear regime. As a result, the period would vary with the amplitude, making it challenging to precisely measure g. Small amplitude ensures that the period is primarily determined by the length of the pendulum or the system's characteristics rather than the amplitude.
By using a small amplitude, we can assume the simple harmonic motion approximation, which simplifies the analysis and provides accurate results for measuring g.