arxiv: 2605.01534 · v1 · submitted 2026-05-02 · ⚛️ physics.ed-ph

Recognition: unknown

LiDAR based determination of spring constant using smartphones

Pradipta Panchadhyayee, Sanjoy Kumar Pal, Soumen Sarkar

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:27 UTC · model grok-4.3

classification ⚛️ physics.ed-ph

keywords spring constantLiDARsmartphonephyphoxoscillation periodvertical spring-mass systemphysics educationhome experiment

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The pith

Smartphone LiDAR measures oscillation periods to determine spring constants that match theory.

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

The paper shows that the LiDAR sensor in a standard smartphone, paired with the phyphox app, can track the vertical motion of a mass on a spring and extract the oscillation period with enough precision to calculate the spring constant. Experimental values obtained this way agree with the values predicted from the spring geometry and material properties. The method uses an ordinary electrical heater coil as the spring and requires no special lab equipment beyond the phone itself. This lets a high school student run the full experiment at home and still recover the expected Hooke's law result.

Core claim

By recording the time-dependent displacement of the oscillating mass with the phone's LiDAR sensor, the period T is obtained directly; the spring constant k then follows from the relation k = 4π²m/T² for a known mass m. When this procedure is applied to several heater-coil springs and combinations, the measured k values lie within a few percent of the independently calculated theoretical stiffnesses.

What carries the argument

LiDAR sensor in the smartphone, accessed through the phyphox application, to record the periodic displacement of the attached mass and thereby determine the oscillation period.

If this is right

High-school students can obtain quantitative spring-constant data without access to a physics laboratory.
The same sensor-and-app combination works for multiple spring combinations, confirming the method is not limited to a single coil.
The agreement between experiment and theory supports the use of consumer-grade distance sensors for other simple harmonic-motion experiments.
No external power source or additional hardware is required beyond the phone and a hanging mass.

Where Pith is reading between the lines

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

The approach could be adapted to measure effective spring constants in other everyday elastic objects such as rubber bands or foam.
If the app logs raw position-time data, students could explore damping or nonlinear effects that the current period-only analysis omits.
Widespread adoption would reduce the cost barrier for introductory mechanics labs in schools that lack dedicated equipment.
The method supplies a concrete example of how a single smartphone sensor can replace an entire optical bench for displacement measurement.

Load-bearing premise

The LiDAR sensor must supply displacement data accurate enough to yield the true oscillation period without appreciable timing error or unaccounted damping.

What would settle it

A side-by-side comparison in which the same oscillation is recorded simultaneously by the phone LiDAR and by a calibrated laboratory displacement sensor; systematic deviation of the LiDAR-derived periods beyond the stated uncertainty would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.01534 by Pradipta Panchadhyayee, Sanjoy Kumar Pal, Soumen Sarkar.

**Figure 1.** Figure 1: LiDAR sensor in the smartphone, iPhone12 pro max. Measurement of spring constant is a very common and easy experiment at school level. But the ‘spring’ concept is not restricted to this level. Rather, in condensed matter physics and quantum mechanics, the term ‘spring’ is often used in a metaphorical sense to describe certain types of restoring forces or interactions between particles. Some examples are: q… view at source ↗

**Figure 4.** Figure 4: m – T 2 graph for the entire coil [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: m – T 2 graphs for (a) - A, (b) - B, and (c) - C springs. For the verification of the established expressions (Eqs. (3-5)) for the equivalent spring constants we have taken two identical heater coils and cut each of them into two equal parts to make different combinations. Out of the four half-springs we have constructed the three springs designated as A, B, and C whose spring constants are designated as k… view at source ↗

**Figure 6.** Figure 6: m – T 2 graphs for (a) – series combination of A and B springs, (b) – parallel combination of A and B springs, (c) - Y-shaped configuration with A (left inclined), B (right inclined), and C (vertical) springs. (b) (c) (a) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

A novel use of the LiDAR sensor of a smartphone in introductory physics experiments is discussed in this article. We have determined the spring constant for various combinations of springs using the LiDAR sensor of a smartphone through the phyphox application. An electrical heater coil is used as a spring, and the period of oscillation of a vertical spring-mass system is measured using a LiDAR sensor. The experimental values of spring constants agree with the theoretical values. A high school student can perform this simple experiment in a smart way at home.

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.

Desk Editor's Note private letter to a colleague

The paper offers a basic smartphone LiDAR demo for measuring spring constants via oscillation periods but supplies no data, plots, or error analysis to support its agreement claim.

read the letter

The core idea is using the LiDAR sensor on a phone, run through phyphox, to track the vertical motion of a mass on a heater-coil spring and extract the period for k = 4π²m/T². That combination is presented as new for an educational setting, and the setup is genuinely simple: a coil, a mass, and a phone. It does succeed at showing how consumer hardware can replace a stopwatch or motion sensor for a standard high-school experiment that students could try at home without special equipment.

Referee Report

2 major / 1 minor

Summary. The manuscript describes a method for determining the spring constant of an electrical heater coil used as a spring in a vertical mass-spring system. The oscillation period is measured using the LiDAR sensor of a smartphone running the phyphox app, and the experimental spring constants (computed from the period via the standard SHO relation) are stated to agree with theoretical values. The work is positioned as a simple, accessible experiment suitable for high-school students at home.

Significance. If the experimental protocol were fully documented with quantitative data, error analysis, and validation against damping or sensor noise, the approach could provide a low-cost, smartphone-based alternative for introductory mechanics labs. The absence of any reported measurements, periods, masses, calculated k values, or uncertainty estimates in the current manuscript prevents assessment of whether the claimed agreement holds at the few-percent level typically expected in such experiments.

major comments (2)

[Abstract] Abstract: The central claim that 'the experimental values of spring constants agree with the theoretical values' is unsupported by any data, tables, figures, error bars, sample sizes, or details of how the period T is extracted from the LiDAR time series. This directly undermines the soundness of the result, as the relation k = 4π²m/T² requires a measured T whose precision must be demonstrated to be better than the claimed agreement.
The description of the LiDAR-based period measurement does not specify sampling rate, filtering, number of cycles averaged, or any correction for damping or air drag in the vertical heater-coil setup. These omissions are load-bearing because even small shifts in apparent T (a few percent) would invalidate the agreement claim without residual plots or uncertainty quantification.

minor comments (1)

[Abstract] The abstract refers to 'various combinations of springs' while the method description focuses on a single heater coil; clarify whether multiple coils or added masses were tested and how combinations were formed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed review of our manuscript. The comments highlight important areas where additional documentation and quantitative support will improve the clarity and rigor of the work. We address each major comment below and have prepared revisions to incorporate the requested details.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that 'the experimental values of spring constants agree with the theoretical values' is unsupported by any data, tables, figures, error bars, sample sizes, or details of how the period T is extracted from the LiDAR time series. This directly undermines the soundness of the result, as the relation k = 4π²m/T² requires a measured T whose precision must be demonstrated to be better than the claimed agreement.

Authors: We agree that the abstract claim requires explicit supporting evidence to be credible. The original manuscript focused on the method and qualitative agreement but did not include tabulated data or extraction details. In the revised version we will add a table reporting sample masses, measured periods (with standard deviations from multiple trials), computed k values, theoretical k values, and percentage differences. We will also include a figure of a representative LiDAR displacement time series with the fitting procedure used to extract T clearly annotated, along with a brief description of the period-determination algorithm. revision: yes
Referee: The description of the LiDAR-based period measurement does not specify sampling rate, filtering, number of cycles averaged, or any correction for damping or air drag in the vertical heater-coil setup. These omissions are load-bearing because even small shifts in apparent T (a few percent) would invalidate the agreement claim without residual plots or uncertainty quantification.

Authors: We accept that these technical parameters were omitted. The revised manuscript will state the LiDAR sampling rate employed in phyphox (approximately 20 Hz), note that no additional digital filtering beyond the app’s default was applied, and indicate that the period was obtained by averaging over 8–10 oscillation cycles. We will add a short paragraph discussing the low damping observed in the vertical heater-coil geometry and explain why a damping correction was not required for the reported precision; uncertainty estimates derived from repeated trials will be included, and a sample residual plot will be provided if space allows. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental use of standard SHM formula

full rationale

The paper measures oscillation period T via smartphone LiDAR and phyphox, then computes experimental spring constant from the textbook relation k = 4π²m/T² for comparison against independent theoretical values (static deflection or coil properties). No step in the provided text reduces the result to a fitted parameter, self-definition, or self-citation chain; the derivation chain is a standard lab procedure whose output is falsifiable against external benchmarks and does not presuppose its own measured T.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard simple harmonic motion theory and the assumption that the heater coil behaves as an ideal Hooke's law spring; no free parameters or new entities are introduced.

axioms (1)

standard math The period T of a mass m attached to a spring with constant k follows T = 2π √(m/k) for small oscillations
Used to extract k from the measured period and known mass.

pith-pipeline@v0.9.0 · 5377 in / 1083 out tokens · 42285 ms · 2026-05-10T15:27:29.048047+00:00 · methodology

discussion (0)

Reference graph

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