What sets the swing?

Learning goal

Students collect three ten-cycle timings at each of three prepared lengths, calculate period automatically, compare means and observed ranges, and explain the length–period relationship. They distinguish a complete cycle from a half-swing and understand why timing several cycles reduces the effect of start/stop timing error on each calculated period.

Prerequisites: time per cycle, control variables, means, and seconds versus meters/centimeters. Square-root proportionality can be introduced during the debrief. Allow roughly 15–25 minutes for the activity, plus discussion; this is a planning estimate.

Procedure

Predict the effect of increasing length on period.
Place stand, string/clamp, 100 g bob, ruler, and stopwatch.
Set and verify the prepared 25 cm pivot-to-bob-center length.
Release from 10° without a push. The app times ten complete cycles with simulated reaction offsets.
Repeat three trials at 25 cm. Set 50 cm and then 100 cm, with three trials at each. Fixed mass, release angle, and gravity remain unchanged.
Compare mean periods and observed ranges. Support a conclusion with two measured means and units.
Optionally rearrange T = 2π√(L/g) to estimate g using the 100 cm mean period.

A five-second animation compresses the ten-cycle interval. The stopwatch models the full elapsed time; it does not measure real time or the student’s clicking speed. Students who prefer reduced motion see a static apparatus while the trial is collected.

Expected pattern and assessment

The ideal small-angle periods are approximately 1.003 s at 25 cm, 1.419 s at 50 cm, and 2.006 s at 100 cm. A fourfold length increase approximately doubles the period; doubling the length multiplies the period by √2. These are model predictions, not numbers students must reproduce exactly.

A start/stop offset difference of up to ±0.30 s on a ten-cycle timing changes the calculated period by up to about ±0.030 s, plus display rounding. Assess the pattern and evidence rather than exact agreement with the ideal values.

Claim: longer tested lengths had longer periods under the fixed conditions.
Evidence: cites at least two relevant mean periods in seconds and their lengths.
Reasoning: connects the comparison to square-root dependence; the longer period means slower rhythm, not faster motion per cycle.
Limit: identifies an assumption or untested variable and explains why it matters.

Answer choices and the optional calculation are checked automatically. Written scientific reasoning requires teacher review. Use the shared review checklist on the teacher overview; no writing score is automatically assigned.

Discussion prompts

Why is traveling from one side to the other not a full cycle?
How would a 0.20 s timing error affect a one-cycle period versus a ten-cycle average period?
Does timing ten swings eliminate a consistently mismeasured length?
Can this experiment show whether bob mass affects period? What new controlled investigation would you need?
Why does a stopwatch display of 0.01 s not mean timing accuracy is ±0.01 s?

Model and limitations

The model uses T = 2π√(L/9.81), with L in meters. The string is massless and inextensible, the bob is a point mass, and prepared lengths are exact. There is no drag, pivot friction, damping, or finite-angle correction. The fixed 10° release is represented by the small-angle approximation.

Each trial adds independent uniform start and stop reaction offsets within ±0.15 s; recorded ten-cycle time equals 10T + stop offset − start offset, rounded to 0.01 s. The period is recorded time divided by ten. This is explicit numerical variation, not a validated model of a particular student’s reaction time. Observed ranges are not confidence intervals.

The optional g estimate uses 4π²L/T². Because timings include variation, it may differ from 9.81 m/s². A match does not validate a real apparatus: the data were generated using the same ideal equation. The experiment changes only length and cannot establish mass or angle dependence.

Students can open the printable report from results or Lab options, add name/class, and print or save as PDF. Progress is browser-local; save the report before restarting or changing devices. Real suspended masses and apparatus require teacher supervision.