The use case of an asymptotic matching method in physics: large-angle pendulum

Abstract This paper examines the calculation of the period of a simple pendulum in the case of extremely large amplitude movements. The calculation is carried out using the method of asymptotic matching, which allows obtaining analytical solutions for the pendulum period that contrast very well with the values found through numerical integration. This analysis can be of great use to undergraduate and graduate students in physical sciences, as it provides mathematical tools that are highly useful in the fields of physical and mathematical sciences. These tools can be applied to a range of more complex problems in areas such as quantum mechanics, fluid mechanics, and related fields.