Oscillation period of the truncated simple pendulum

Abstract

In this manuscript, a non typical kind of simple pendulum called Truncated Simple Pendulum is analysed to obtain its oscillation period, frequency, and angular frequency. It is easily derived that its motion can be viewed as the concatenation of two pendular movements with different lengths, contributing each one to half of the period of the complete oscillation. An analytical formulation is derived and corroborated with an experiment showing high agreement. This experiment could be interesting as a proposed exercise for the students or as a laboratory practical work. Besides, the gravity acceleration can be determined from each singular experiment and averaged to obtain it with lesser experimental error. In addition, it can be used to evaluate energy conservation theorem and small angle approximation (Law of isochronism) for the pendular oscillation. The level of the manuscript makes it appropriate for undergraduate students and introductory physics courses.