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PhysicsPhysics Scientific InvestigationSL

How the length of a simple pendulum affects its period

A well-run investigation that linearises the relationship correctly, but the uncertainties aren't carried through to the gradient and the conclusion isn't yet compared with g. (Science estimates are the least reliable, so treat this as a wide guide.)

~2650 words · Up to 3,000 words. Charts, tables, equations, citations and the bibliography don't count.

Estimated

12–16

out of 24

Decent
AI estimate — not an official IB grade.

Draft history

How this commentary developed, draft by draft — a record you can show your teacher.

Draft 1

20 Aug 2026

11/24
A 3/6B 2/6C 4/6D 2/6

~2300 words

3/3 checklist done

14/24+3
A 3→4/6B 2→3/6C 4/6D 2→3/6

~2650 words

0/3 checklist done

Focus on these first

The highest-impact changes, in order.

1

Carry uncertainties through to the gradient

Propagate the timing uncertainty into T², add error bars, and use max/min lines to quote the gradient's uncertainty.

Data analysis (Criterion B)

2

Compare g with the accepted value

Quote a percentage error against 9.81 m s⁻² and say whether it lies within your uncertainty.

Conclusion (Criterion C)

3

Rank your sources of error

Explain how much each weakness affects g, strongest first, and match each improvement to the error it fixes.

Evaluation (Criterion D)

Comments on your text

Working wellProblemSuggestion

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This investigation examines how the length of a simple pendulum affects its period of oscillation. The length of the pendulum was varied from 0.20 m to 1.00 m in steps of 0.20 m1, and the mass of the bob and the amplitude were kept constant. The time for ten oscillations was measured three times at each length and averaged, then divided by ten to find the period. A graph of T² against L was plotted, giving a straight line through the origin2. The gradient was used to calculate a value for g of 9.6 m s⁻²3. Human reaction time when starting and stopping the timer is a systematic source of error.

Criterion breakdown

Criterion A

Research design

4 / 6

DecentMedium confidence

How to improve

  • Justify the length range and why ten oscillations were timed
  • State how the amplitude was kept small and constant

To reach 5/6

Explain why the length range and oscillation count were chosen, and how amplitude was controlled.

Criterion B

Data analysis

3 / 6

DecentMedium confidence

How to improve

  • Add error bars and max/min gradient lines, and quote the gradient's uncertainty
  • Propagate the timing uncertainty into T²

To reach 4/6

Propagate uncertainties into T² and show them as error bars with a max/min gradient so the gradient's uncertainty is quantified.

Tables, graphs and figures

Image 1 · Linearised graph with a line of best fit

Figure 1 — T² against pendulum length

Processed data section

Good
  • Add vertical error bars from the spread of repeats
  • Draw max/min gradient lines and quote the gradient uncertainty

Criterion C

Conclusion

4 / 6

DecentMedium confidence

How to improve

  • Compare your g with the accepted 9.81 m s⁻² as a percentage error
  • State whether the accepted value lies within your uncertainty range

To reach 5/6

Compare your value of g quantitatively with the accepted value and judge the agreement against your uncertainty.

Criterion D

Evaluation

3 / 6

DecentMedium confidence

How to improve

  • Rank the errors by their impact on g
  • Explain how a light gate would reduce the dominant error

To reach 4/6

Explain the relative impact of each weakness on g and tie each improvement to the error it addresses.

What's already working

  • Correct linearisation of the relationship
  • A reproducible method with controlled variables
  • Gradient used correctly to find g
  • Specific, realistic evaluation

Revision Checklist

0 / 3 done