Refining Gravity Estimation in the Simple Pendulum Experiment using Microcontroller

Abstract

The simple pendulum is a basic experiment performed in undergraduate laboratory to determine the value of acceleration due to gravity ‘g’ by studying simple harmonic motion. The experiment requires continuous monitoring of the pendulum oscillations to measure its time-period with the help of a stop watch. This task, though simple, becomes cumbersome when the students are asked to take several numbers of readings to decrease random error. In this work, we have automated this experiment with the help of a light dependent resistor (LDR), laser light and microcontroller, Arduino. For this purpose, a voltage divider circuit is designed using LDR (with aperture pointed by a laser light). This setup is kept across the pendulum bob so that bob can block the light from laser to reach LDR. The LDR is then connected to analog pin of the Arduino to record voltage across it. When the pendulum begins oscillations, the laser beam is blocked by the bob at regular intervals of time and voltage across the LDR also varies with it. By measuring this change in voltage, the controller is programmed to measure the time-period of the oscillations. By programming, we have been able to take large number of readings. The readings obtained by this setup are observed to be more accurate and precise as compared to the manual readings. Manually the value of ‘g’ is found to be 10.31 ± 1.03 m/s² but with Arduino setup it was observed to be 9.77 ± 0.006 m/s².