Improved Accuracy in Calculating Acceleration due to Earth’s Gravity using Taylor Series Expansion: A case study in Pendulum Oscillations
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Abstract
This study examined the simple harmonic motion of a pendulum oscillating at five different string lengths (0.2, 0.4, 0.6, 0.8, and 1.0 meters) at four different angles (10°, 20°, 30°, and 50°). A photogate sensor was used to measure the period. A high-accuracy formula and a simple formula were then used to compute the gravitational acceleration. The results showed that the period relates to the length of the string and was comparable at oscillation angles of 10°, 20°, and 30°. However, raising the angle to 50° extended the time. It was also found that using a 0.2-meter-long thread caused the most error in gravitational acceleration estimations. Using either a simple or a high-accuracy formula to calculate gravitational acceleration results in minimal changes in error levels for angles smaller than 10°. However, when the angle was extended to 20°, 30°, and 50°, calculations utilizing a high-accuracy formula were shown to be far more precise and error-free than those using a simple formula.
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