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arxiv: 2503.23506 · v4 · submitted 2025-03-30 · ⚛️ physics.ed-ph

Integrating Artificial Neural Networks into Undergraduate Physics Laboratory: A Compound Pendulum Case Study

Saralasrita Mohanty , Prabhu Prasad Tripathy , Raja Das , Sudakshina Prusty This is my paper

Pith reviewed 2026-05-22 22:56 UTC · model grok-4.3

classification ⚛️ physics.ed-ph
keywords artificial neural networkscompound pendulumundergraduate physics labgravitational accelerationmachine learning educationdata analysisregression
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The pith

An artificial neural network trained on compound pendulum data reproduces the measured value of gravitational acceleration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates the integration of an artificial neural network into the compound pendulum experiment typically used to find the acceleration due to gravity in undergraduate labs. Students first perform the standard measurements and analytical calculation of g, then use those data to train, validate, and test an ANN model. The network achieves very close agreement with the experimental result, indicating it has captured the relationship between the input parameters and g. This serves to teach students about regression, validation, and data-driven techniques in a physics context without claiming to enhance the accuracy of the measurement itself.

Core claim

The analytical method yields g = 1009.03 ± 6.82 cm/s². The ANN, trained on the same experimental dataset split into 70% training, 15% validation, and 15% testing, predicts a mean g of 1009.029858 cm/s² with a mean absolute error of 0.000592 cm/s². The close match shows the ANN has learned the mapping from pendulum parameters to g, functioning as an educational tool for machine learning concepts in experimental physics rather than a replacement for analytical methods.

What carries the argument

The artificial neural network model that takes effective length, time period, and angular displacement as inputs to predict g, trained on the experimental dataset.

If this is right

  • The ANN introduces students to regression, validation, overfitting, and data-driven analysis using real experimental data.
  • It complements the conventional analytical method for determining g.
  • The method provides a practical way to illustrate how machine learning supports data analysis in physics laboratories.
  • Students gain experience applying computational tools alongside traditional experimental techniques.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar ANN modules could be added to other standard undergraduate experiments to build consistent exposure to data analysis methods.
  • Students might later apply the trained model to check the consistency of new measurements they collect.
  • The educational benefit could be tested by comparing learning outcomes in labs with and without the ANN component.

Load-bearing premise

The data obtained from the compound pendulum experiment are suitable and sufficient to train an ANN that illustrates the desired machine learning concepts.

What would settle it

Train the ANN on one set of compound pendulum measurements and then apply it to an independent set collected under different conditions; large prediction errors would indicate the model did not learn a general relationship.

Figures

Figures reproduced from arXiv: 2503.23506 by Prabhu Prasad Tripathy, Raja Das, Saralasrita Mohanty, Sudakshina Prusty.

Figure 1
Figure 1. Figure 1: Fig.1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fig.2. A neural network architecture for predicting the acceleration due to gravity (g) from experimental [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The relationship between T and the distance from the pivot point to the center of mass is [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fig.3. Sample graph for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Correlation Coefficient vs. Number of Nodes for Training, Validation, Test, and Overall Datasets [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Regression plots illustrating the comparison between neural network predictions and experimental [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The histogram plot illustrates the distribution of error values for ’g’ during the training, valida [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The performance of the artificial neural network model was assessed based on the mean squared [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Artificial Neural Networks (ANNs) are becoming important tools in physics research and education because they help in data analysis and complement traditional analytical methods. In this work, ANN modeling is introduced in a standard compound pendulum experiment used to determine the acceleration due to gravity, g. The aim is not to replace the conventional analytical method, but to demonstrate how machine learning can support experimental data analysis in undergraduate physics laboratories. Students first measure parameters such as effective length, time period, and angular displacement, and determine g using standard analytical methods with uncertainty analysis. These experimentally obtained data are then used to train and test an ANN model. The dataset is divided into training (70%), validation (15%), and testing (15%) groups. The experimentally determined value of gravitational acceleration was 1009.03 +/- 6.82 cm/s^2, while the ANN predicted a mean value of 1009.029858 cm/s^2 with a mean absolute error of 0.000592 cm/s^2. The close agreement between the experimental and ANN-predicted values shows that the ANN successfully learned the relationship between the pendulum parameters and g. However, the ANN prediction error should not be considered as an improvement in experimental accuracy because the model is trained using experimentally derived data. Instead, the ANN serves as a useful computational and educational tool that introduces students to regression, validation, overfitting, and data-driven analysis alongside traditional experimental physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript describes an educational case study integrating artificial neural networks into an undergraduate compound pendulum experiment for determining g. Students collect data on effective length, time period, and angular displacement, compute g analytically with uncertainty analysis (reported as 1009.03 ± 6.82 cm/s²), then train an ANN on the same dataset using a 70/15/15 train/validation/test split. The ANN produces a mean prediction of 1009.029858 cm/s² with MAE 0.000592 cm/s². The authors explicitly state that this close agreement does not indicate improved experimental accuracy, as the model is trained on experimentally derived targets, but instead serves to illustrate regression, validation, overfitting, and data-driven methods alongside traditional analysis.

Significance. If the described approach holds, the work provides a concrete, replicable template for introducing machine learning concepts into standard undergraduate physics laboratories without displacing analytical methods. The explicit caveat that the low MAE does not represent enhanced accuracy is a notable strength, as it models responsible use of data-driven tools and avoids overclaiming physical insight from fitting.

minor comments (2)
  1. [Abstract] Abstract: The ANN-predicted mean is reported to nine decimal places while the experimental value uses two; consider aligning significant figures or adding a brief note on displayed precision for consistency with the experimental uncertainty of ±6.82 cm/s².
  2. [Abstract] Abstract: The dataset split is described as 70/15/15 but the text does not specify whether the split is random, stratified, or otherwise; a short clarification on the splitting procedure would aid reproducibility in an educational context.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents an educational demonstration of training an ANN for regression on compound-pendulum data. Inputs (L_eff, T, amplitude) are measured experimentally; targets (g) are computed from those same inputs via the standard analytical formula; the ANN is then trained on the resulting (input, target) pairs and evaluated on a held-out split. The reported low MAE is the expected outcome of supervised learning on a deterministic mapping and is explicitly caveated by the authors as not constituting improved experimental accuracy. No derivation chain, first-principles claim, or uniqueness theorem is advanced; the work contains no self-citations, no ansatz smuggling, and no renaming of known results. The central pedagogical claim is self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; full manuscript details unavailable. No free parameters or invented entities are described. The central claim rests on the assumption that ANN training on experimental data can serve an educational purpose without claiming superior accuracy.

axioms (1)
  • domain assumption Artificial neural networks can be trained on experimental measurements to approximate the mapping from pendulum parameters to gravitational acceleration.
    Invoked when the authors state that the ANN learned the relationship between parameters and g.

pith-pipeline@v0.9.0 · 5797 in / 1199 out tokens · 90164 ms · 2026-05-22T22:56:23.206136+00:00 · methodology

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

  1. [1]

    J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems , 5th ed. (Brooks Cole, 2004)

    work page 2004

  2. [2]

    Barger and M

    V. Barger and M. Olsson, Classical Mechanics: A Modern Perspective , 2nd ed. (McGraw-Hill, 1995)

    work page 1995

  3. [3]

    J. R. Taylor, Classical Mechanics (University Science Books, 2005)

    work page 2005

  4. [4]

    Huygens, Horologium Oscillatorium (F

    C. Huygens, Horologium Oscillatorium (F. Muguet, Paris, 1673)

    work page

  5. [5]

    R. C. Hibbeler, Engineering Mechanics: Dynamics , 14th ed. (Pearson, 2017)

    work page 2017

  6. [6]

    Beitz and K.-H

    W. Beitz and K.-H. K¨ uttner,Engineering Design: A Systematic Approach , 3rd ed. (Springer, 2007)

    work page 2007

  7. [7]

    W. H. Green, ”Using a compound pendulum to measure the acceleration due to gravity,” Am. J. Phys. 65, 792-795 (1997)

    work page 1997

  8. [8]

    Ganci, ”Experiments with a compound pendulum: Moment of inertia and acceleration of gravity,” Phys

    S. Ganci, ”Experiments with a compound pendulum: Moment of inertia and acceleration of gravity,” Phys. Educ. 29, 123-126 (1994)

    work page 1994

  9. [9]

    Stark, ”The compound pendulum and the precision of the second pendulum,” Phys

    H. Stark, ”The compound pendulum and the precision of the second pendulum,” Phys. Teach. 44, 589-590 (2006)

    work page 2006

  10. [10]

    A. H. Cook, ”A new absolute determination of the acceleration due to gravity at the National Physical Laboratory,” Nature 208, 279 (1965)

    work page 1965

  11. [11]

    Walker, Fundamentals of Physics—Halliday Resnick , 10th ed

    J. Walker, Fundamentals of Physics—Halliday Resnick , 10th ed. (Wiley, Hoboken, NJ, 2015)

    work page 2015

  12. [12]

    Siebert, P

    C. Siebert, P. R. DeStefano, and R. Widenhorn, ”Comparative modeling of free fall and drag- enhanced motion in the classical physics drop experiment,” Eur. J. Phys. 40, 045004 (2019)

    work page 2019

  13. [13]

    Harnsoongnoen, S

    S. Harnsoongnoen, S. Srisai, P. Kongkeaw, and T. Rakdee, ”Improved accuracy in determining the acceleration due to gravity in free fall experiments using smartphones and mechanical switches,” Appl. Sci. 14, 2632 (2024). doi:10.3390/app14062632

    work page doi:10.3390/app14062632 2024

  14. [14]

    (BIPM, 2019)

    Bureau International des Poids et Mesures (BIPM), The International System of Units (SI) , 9th ed. (BIPM, 2019)

    work page 2019

  15. [15]

    Khongiang, A

    L. Khongiang, A. Dkhar, and S. Lato, ”Accurate determination of acceleration due to gravity, g in Shillong using electronic timer,” Int. J. Geol. Earth Environ. Sci. 5, 105-111 (2015)

    work page 2015

  16. [16]

    Lamb, Cold Atom Gravity Gradiometer for Field Applications , Ph.D

    A. Lamb, Cold Atom Gravity Gradiometer for Field Applications , Ph.D. thesis, University of Birm- ingham, 2018

    work page 2018

  17. [17]

    A. D. Dongare, R. R. Kharde, and A. D. Kachare, ”Introduction to artificial neural network,” Int. J. Eng. Innov. Technol. 2, 189-194 (2012)

    work page 2012

  18. [18]

    T. K. Gupta and K. Raza, ”Optimization of ANN architecture: A review on nature-inspired tech- niques,” in Machine Learning in Bio-Signal Analysis and Diagnostic Imaging , pp. 159-182 (2019)

    work page 2019

  19. [19]

    R. V. Woldseth, N. Aage, J. A. Bærentzen, and O. Sigmund, ”On the use of artificial neural networks in topology optimization,” Struct. Multidiscip. Optim. 65, 294 (2022)

    work page 2022

  20. [20]

    Zhang et al., ”Application of AI in Experimental Physics,” J

    D. Zhang et al., ”Application of AI in Experimental Physics,” J. Phys. Educ. (2020)

    work page 2020

  21. [21]

    Niyogi, F

    P. Niyogi, F. Girosi, and T. Poggio, ”Incorporating prior information in machine learning by creating virtual examples,” Proc. IEEE 86, 2196-2209 (1998)

    work page 1998

  22. [22]

    T. R. Kane and D. A. Levinson, ”Dynamics Theory and Applications: The Compound Pendulum,” Am. J. Phys. 42, 738–745 (1974). doi:10.1119/1.1987889

    work page doi:10.1119/1.1987889 1974

  23. [23]

    Cuomo, V

    S. Cuomo, V. Schiano Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, ”Scientific machine learning through physics-informed neural networks: Where we are and what’s next,” J. Sci. Comput. 92, 88 (2022). 17

    work page 2022

  24. [24]

    Schmidhuber, Deep learning in neural networks: An overview, Neural Networks 61 (2015) 85 – 117

    J. Schmidhuber, ”Deep Learning in Neural Networks: An Overview,” Neural Networks 61, 85-117 (2015).doi:10.1016/j.neunet.2014.09.003

    work page doi:10.1016/j.neunet.2014.09.003 2015

  25. [25]

    D. E. Rumelhart, G. E. Hinton, and R. J. Williams, ”Learning representations by back-propagating errors,” Nature 323, 533-536 (1986)

    work page 1986

  26. [26]

    Y. C. Wu and J. W. Feng, ”Development and application of artificial neural network,” Wirel. Pers. Commun. 102, 1645-1656 (2018)

    work page 2018

  27. [27]

    A. S. V., R. Das, M. S. S. et al., ”Prediction of Zn concentration in human seminal plasma of normospermia samples by artificial neural networks (ANN),” J. Assist. Reprod. Genet. 30, 453–459 (2013). doi:10.1007/s10815-012-9926-4 18

    work page doi:10.1007/s10815-012-9926-4 2013