Deriving Gravitational Acceleration from pendulum oscillation with rotational motion by the arbitrary amplitude method (2020)

The pendulum is an object suspended from a pivot by a string that can be utilized to calculate gravitational acceleration. However, most works utilize the sine small angle approximation formula, hence producing much inaccuracy. Instead, energy conservation is utilized to derive an equation of the period for arbitrary amplitudes. Furthermore, the ideal model of a pendulum has a period only dependent upon length of the string and gravitational acceleration, one in the real world is affected by air resistance, rotation of the bob and other external factors. Hence, within this report, I aim to develop the arbitrary-amplitude method to take energy used for rotation into consideration, and derive the gravitational acceleration of Earth.