Determining Gravitational Acceleration with the Mathematical Pendulum Swing Method
Keywords:
Gravitational Acceleration, Mathematical Pendulum, Pendulum Swing, Swing MethodAbstract
Pendulum-derived gravitational acceleration values vary unpredictably due to unquantified string length and initial angle dependencies. This study aims to assess the feasibility and precision of the mathematical pendulum swing method in measuring gravitational acceleration. The research investigates the relationship between the pendulum’s string length, oscillation period, and initial deviation angle. It is hypothesized that longer strings will result in slower oscillations while shorter strings produce faster motions. Additionally, the study examines how these factors collectively impact gravitational acceleration measurement. Through controlled experiments, the study’s goal is to determine the precision of the pendulum swing method in determining gravitational acceleration and the factors influencing its reliability. Results demonstrate that a simple mathematical pendulum accurately determines gravitational acceleration with a calculated value of approximately 9.95974m/s². The findings confirm that the square of the oscillation period is directly proportional to the string length (T² ∝ l) and emphasize the importance of maintaining the initial deviation angle under 10 degrees to ensure measurement accuracy. These findings reinforce the pendulum’s utility in physics education and affordable gravitational field assessment, particularly in resource-limited settings. The study provides a foundational framework for improving experimental accuracy in classical mechanics and highlights the method’s enduring relevance in scientific pedagogy and fundamental research.
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References
Amedeker, M. K. (2022). Simple pendulum experiment: Angular approximation revisited. European Journal of Education and Pedagogy, 3(3), 33–35. https://doi.org/10.24018/ejedu.2022.3.3.248
Fauzi, A., Marwoto, P., & Nugroho, S. E. (2024). A complete arduino-based mathematical pendulum experiment tool with real-time data acquisition using an excel spreadsheet. JIPF (Jurnal Ilmu Pendidikan Fisika), 9(2), 211. https://doi.org/10.26737/jipf.v9i2.5073
Gea, E. H., Pattiserlihun, A., & Sudjito, D. N. (2022). Golabz-based interactive learning design about simple harmonic motion on pendulum swing. Jurnal Inovasi Pendidikan IPA, 8(2), 185–198. https://doi.org/10.21831/jipi.v8i2.42962
Ismail, A. I. (2020). New vertically planed pendulum motion. Mathematical Problems in Engineering, 2020, 1–6. https://doi.org/10.1155/2020/8861738
Kidd, R. B., & Fogg, S. L. (2002). A simple formula for the large-angle pendulum period. The Physics Teacher, 40(2), 81–83. https://doi.org/10.1119/1.1457310
Lekner, J. (2004). Pendulum with a uniformly heavy cord. American Journal of Physics, 54(2), 112–121.
Mohammad Bakhit Mufti, Mutakinati, L., & Nadia Dewi Masithoh. (2022). Analysis of physics concepts in adrenaline games in the Batu Night Spectacular (BNS) area. Studies in Philosophy of Science and Education, 3(1), 30–40. https://doi.org/10.46627/sipose.v3i1.271
Nelson, R. A., & Olsson, M. G. (1986). The pendulum—Rich physics from a simple system. American Journal of Physics, 54(2), 112–121. https://doi.org/10.1119/1.14703
Neslušan, L. (2023). Component x of the gravitational acceleration in general relativity and concept of mass. Contributions of the Astronomical Observatory Skalnaté Pleso, 53(2). https://doi.org/10.31577/caosp.2023.53.2.16
Oliveira, V. (2016). Measuring g with a classroom pendulum using changes in the pendulum string length. Physics Education, 51(6), 063007. https://doi.org/10.1088/0031-9120/51/6/063007
Pratidhina, E., Yuliani, F. R., & Dwandaru, W. S. B. (2020). Relating simple harmonic motion and uniform circular motion with tracker. Revista Mexicana de Física E, 17(2 Jul-Dec), 141–145. https://doi.org/10.31349/RevMexFisE.17.141
Pujol, O. (2010). The pendulum: A case study in physics. American Journal of Physics, 78(12), 1302–1310.
Rini, N. W., & Saefan, J. (2023). Hamilton equations of pendulum-spring system. Lontar Physics Today, 2(2), 85–91. https://doi.org/10.26877/lpt.v2i2.17312
Rivera-Figueroa, A., & Lima-Zempoalteca, I. (2021). Motion of a simple pendulum: A digital technology approach. International Journal of Mathematical Education in Science and Technology, 52(4), 550–564. https://doi.org/10.1080/0020739X.2019.1692934
Sardjito, & Yuningsih, N. (2020). The period of physical pendulum motion with large angular displacement. Proceedings of the International Seminar of Science and Applied Technology (ISSAT 2020). https://doi.org/10.2991/aer.k.201221.034
Silvi Mutia, Roslita Anggraeni, Yunda Wahyuning Tyas, Khalda Naila, Satria Firmansah, & Yuni Ratna Sari. (2024). Analisis pengaruh hambatan gaya gravitasi melalui parasut sederhana. Jurnal Nakula : Pusat Ilmu Pendidikan, Bahasa Dan Ilmu Sosial, 2(4), 295–304. https://doi.org/10.61132/nakula.v2i4.1126
Sudarmanto, A., Poernomo, J. B., & Maulana, A. R. (2023). The IoT-based mathematical pendulum real laboratory tool. Journal of Materials Science, 6(2), 92–103.
Wardani, F. (2020). An analysis of student’s concepts understanding about simple harmonic motion: Study in vocational high school. Journal of Physics: Conference Series, 1511(1), 012079. https://doi.org/10.1088/1742-6596/1511/1/012079
Yuningsih, N., Sardjito, S., & Dewi, Y. C. (2020). Determination of Earth’s gravitational acceleration and moment of inertia of rigid body using physical pendulum experiments. IOP Conference Series: Materials Science and Engineering, 830(2), 022001. https://doi.org/10.1088/1757-899X/830/2/022001
