Pendulum Lab: Measuring and Reducing Uncertainty, Comparing Data Sets (3 Parts)

The Week 1 demonstration pendulum should be large and centrally located so all students can see it. Use a protractor mounted at the pivot to set release angles. Release silently with no timing instructions — the resulting messiness in student data (typically spread over several tenths of a second) is the point and motivates everything that follows.

Have students write their individual measurements on the board immediately; this builds a shared class data set and makes the spread viscerally obvious.

In Week 2, put a shared table on the board (or a projected spreadsheet) where groups post their mean, number of consecutive swings, number of trials, standard deviation, and standard uncertainty. This drives productive between-group comparison and helps groups calibrate whether their uncertainty is competitive. Target precision is better than 0.01 s — tell students this is what's needed to potentially distinguish 10° from 20°.

In Week 3, provide the sharing table (T ± δT, t′, interpretation) partway through the session rather than at the start, so groups commit to their own analysis first.

Common pitfalls: students confuse histograms with bar charts — have a reference image handy. Students may conflate "human error" with random uncertainty; spend time on the distinction in Week 1. When timing many consecutive swings, students sometimes lose count — suggest they verbalize or tap counts.

Desmos histogram links are provided in the lab materials, but Google Sheets or Excel also work. No specialized software is required.

The team agreement and color-coded font contributions in the shared Google Doc are easy to underestimate — enforce them early, as they establish accountability and make grading contributions visible.

This is the opening sequence of an introductory mechanics lab and assumes no prior lab experience or statistics knowledge. Students need only basic algebra and a qualitative understanding that pendulums swing — no knowledge of the period formula T = 2π√(L/g) is required or desired. In fact, the instructor notes explicitly say to pretend you don't know the small-angle approximation, since the goal is for students to reason from their own data rather than confirm a textbook result.

The sequence builds cumulatively: Week 1 introduces measurement, uncertainty, and histograms; Week 2 develops uncertainty reduction techniques; Week 3 introduces quantitative comparison (t′) and student-designed experiments. Each week's homework prepares students for the next session.

After this three-week pendulum unit, the course moves to a two-week "Tossed Objects" unit that introduces scientific integrity and model testing, followed by a "Stretchy Objects" unit on research questions and Hooke's law, and finally a multi-week student-designed investigation with presentations. The pendulum sequence thus establishes the foundational experimental reasoning skills — quantifying uncertainty, iterative refinement, evidence-based argumentation — that students apply with increasing independence throughout the rest of the quarter.