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How does the period of a pendulum vary with the number of strings?
- 1 Wuhan Britain-China School
* Author to whom correspondence should be addressed.
Abstract
This article serves as an extension of analysis of a simple pendulum, a typical example of simple harmonic motion and a common topic in high school physics syllabus. Since the analysis of a simple pendulum ignores the mass of the string in order to model the system as a point mass, a more complex pendulum system consisting of heavy strings and a pendulum bob is explored in this article. Based on theoretical analysis of the model, a relationship between the number of strings and the period of the pendulum is investigated. An experiment was also conducted on a pendulum system using copper wire, a glass bob, a stand, clamps, a clip and a stopwatch. To obtain more accurate results, time taken for five periods was measured three times for each number of strings. A graph is drawn based on data acquired from the experiment and the theoretically deduced relationship is therefore verified. Further study of the general expression for the period of an object that cannot be modelled as a point mass oscillating about a fixed axis is involved. Application of the principle that a change in the position of the center of mass of a pendulum causes a change in its period in Big Ben is also discussed along with a brief introduction of its pendulum structure.
Keywords
physics, simple harmonic motion (SHM), pendulum, Big Ben
[1]. Allum, J. and Morris, P. (2023). Physics for the IB Diploma. 3rd ed. London: Hodder Education, pp.313.
[2]. LibreTexts.org. Pendulums. [online] Available at: https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/15%3A_Oscillations/15.05%3A_Pendulums [Accessed 28 June 2024].
[3]. Giancoli, D. (2014). Physics: Principles with Applications. 7th ed. Glenview: Pearson Education, pp.301.
[4]. Britannica.com. Motion of a particle in two or more dimensions. [online] Available at: https://www.britannica.com/science/mechanics/Motion-of-a-particle-in-two-or-more-dimensions [Accessed 25 April 2024].
[5]. Wazir, I. and Garry, T. (2019). Mathematics: Analysis and Approaches Higher Level for the IB Diploma. London: Pearson Education, pp.876.
[6]. Scribber.com. Coefficient of Determination (R²) | Calculation & Interpretation. [online] Available at: https://www.scribbr.com/statistics/coefficient-of-determination/ [Accessed 11 July 2024].
[7]. Wikipedia.org. Big Ben. [online] Available at: https://en.wikipedia.org/wiki/Big_Ben [Accessed 7 July 2024].
[8]. Britannica.com. Big Ben. [online] Available at: https://www.britannica.com/topic/Big-Ben-clock-London [Accessed 7 July 2024].
[9]. Parliament.uk. Facts and figures: Big Ben and Elizabeth Tower. [online] Available at: https://www.parliament.uk/about/living-heritage/building/palace/big-ben/facts-figures/ [Accessed 8 July 2024].
[10]. leftovercurrency.com British predecimal penny coin. [online] Available at: https://www.leftovercurrency.com/exchange/british-pounds/predecimal-withdrawn-pound-sterling-coins/british-predecimal-penny-coin/#:~:text=The%20old%20predecimal%20British%20penny%20is%20a%20large,a%20weight%20of%202%20kilos%20and%20268%20grams. [Accessed 8 July 2024].
[11]. BMumford.com. The Gravity Escapement. [online] Available at: https://www.bmumford.com/clocks/courthouse/escapement/ [Accessed 7 July 2024].
[12]. Jared Owen. (2022) What’s inside Big Ben? (Elizabeth Tower). 21 April. [online] Available at: https://www.youtube.com/watch?v=H3xgBS_kDNw&t=758s [Accessed 4 July 2024].
Cite this article
Yin,V.Z. (2024). How does the period of a pendulum vary with the number of strings?. Theoretical and Natural Science,36,241-251.
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Volume title: Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation
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