Analysing oscillatory motion of simple pendulum, spring-mass system and cantilever system using tracker video analysis

One of the most challenging task to learn and understanding the oscillatory motion is that students need to have the capability to imagine and visualize the association between the movement of an object oscillated in oscillatory motion and the complex mathematical calculation of the movement. However, with Tracker, modeling and analysis of the motion of objects in videos are possible and easy to use simply by overlaying simple dynamical models onto the videos directly. Therefore, this study was conducted for oscillatory motion to analyze the large angles oscillation of simple pendulum using Tracker Video Analysis (TVA) and high speed camera, to determine the viscosity of glycerol, sunflower oil and sugar solution by analyzing the oscillation of the spring–mass system and to find elastic modulus of ABS plastic, steel and aluminium via analyzing damped harmonic oscillation of high frequency vibration from a cantilever system. Combining with the high speed camera that records the motion of pendulum at a frame rate up to 1000 frames per second (fps), analysis of the motion is performed at different angles (10° to 50°) and video qualities. The periods obtained from the experiment are then compared with the exact period expression and Lima and Arun (L&A) approximation in order to determine how well this approach suited for the large angle approximation. Results have shown that when the video qualities improved particularly from 25 fps to 1000 fps, video analysis approach is entirely consistent with L&A approximation. The result at normal rate shows the error of 0.578% at 10° and gradually increased to 2.002% at 50°, compared to the highest frame rate (1000 fps) shows the error of 0.005% at 10° and gradually increased to 0.026% at 50°. For spring-mass system, the experiment was conducted using sunflower oil, glycerol and sugar solution. The oscillations are then recorded at rate 25 fps at different temperature (30 ℃ to 70 ℃). Damping parameter that was determined using curve fitting was used to calculate the viscosity of liquid. Viscosity values using Tracker have proven to be comparable with measured value from expensive instrument (dynamic shear rheometer). The relative errors of viscosity are compared to the measured values are between 4.76% to 8.76% for glycerol, 6.69% to 10.38% for sunflower oil and 8.58% to 9.67% for sugar solution (30 ℃ to 50 ℃). However, relative error gradually increased from 44.37% to 73.07% when the temperature of sugar solution increased from 60 ℃ to 70 ℃. For high frequency vibration of cantilever experiment, the vibration of plastic, aluminium and stainless steel cantilevers were recorded using high frame rate (1000 fps). The damped angular frequencies obtained from Tracker are used to determine the elastic modulus of cantilever. From the experiment, elastic modulus of plastic is 2.10 GPa, stainless steel is 191.22 GPa and aluminium is 70.81 GPa which have good agreement with measured value from other works. Tracker video analysis approach has shown that it can produce better results than using traditional method or expensive measuring equipment. Besides, it is also very interactive as students can analyse the oscillatory motion in real time from the video and inexpensive.

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