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Measurement of resistance coefficients of pendulum motion with balls of various sizes

In order to obtain the damping and resistance coefficients of a pendulum, we constructed an optical system containing a photogate for measuring the speed of the pendulum at the lowest point of motion. The photogate consisted of a photoresistor, a laser, a mechanical body, and a pendulum ball. A 3D printer was used to produce the mechanical body and pendulum balls of various sizes. Furthermore, we used Arduino to automate measurement of the speed at the lowest point of motion and increase the precision. We found that the resistance coefficient was proportional to the size of the balls, regardless of the ball mass, in agreement with the drag equation for a small Reynolds number.