INVESTIGATION OF THE RELATIONSHIP BETWEEN PENDULUM LENGTH AND OSCILLATION PERIOD IN SIMPLE HARMONIC MOTION

Abstract

In this study the relationship between pendulum length and oscillation period of simple harmonic motion was studied within a controlled experimental setup. The general aim of this experiment was to examine the effect on the period of a pendulum when the length of the pendulum was changed. The length of the pendulum was systematically changed and there was no change in the release angle, mass of the bob or the environmental conditions to reduce experimental error. The results indicated that the oscillation period was growing with the increase of pendulum length, which was in accordance with the theoretical length-pendulum formula. The shorter pendulums swung back and forth more rapidly and the longer pendulums took longer because the length of the pendulum had a longer path for the bob to swing back and forth. The trends, indicated on the plots, were very strong positive ones for pendulum length and period, and almost linear ones for the period squared and the length. The results agree with the simple harmonic motion model which a pendulum should follow, namely the period should be proportional to the square root of the pendulum length. The minor differences between observed and theoretical values were thought to be due to the timing error and air resistance and small differences in the angle of release. The study has also confirmed that the length of pendulum is one of the important parameters which influences the oscillation period in S.H.M in overall.