Maths in physics and engineering · Accessible · Dissertation or artefact

When the small-angle approximation fails: a maths EPQ idea

Why it works as an EPQ

A cheap experiment and a numerical model let you find, and justify, the point where the approximation stops being good enough.

Scope and difficulty

Accessible. Accessible. One pendulum, many amplitudes, a numerical model.

The maths

Builds on these A Level topics: Trigonometry · Numerical methods · Differentiation.

You would learn:

• Simple harmonic motion
• Numerical solution of the full equation
• Percentage error

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive the period for small swings using sin θ ≈ θ.
2. Solve the full equation numerically for larger swings.
3. Measure periods at different amplitudes with repeats.
4. Decide what 'fails' means and find the angle.

Pitfalls

• Timing single swings instead of many.
• A definition of 'fails' chosen after seeing results.

Where to start reading

• Search for: large amplitude pendulum period correction
• Search for: pendulum experiment uncertainty timing

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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All maths in physics and engineering ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.