The investigation · Length of a pendulum and its period
How does the length of a simple pendulum (0.20 to 1.00 m) affect its period of oscillation for small amplitudes (under 10°), and what value of g does the relationship give?
Physics worked example: what becomes more explicit?
The comparison below is instructional, not examiner-scored. Use it to see which evidence or reasoning is missing, then check the current criterion wording for your session.
How does the example make research design evidence more explicit? (6-mark criterion)
It justifies timing 20 oscillations and the small-angle limit, which is what makes the method precise and repeatable.
Under-specified
I will change the length of the string and time the swings with a stopwatch.
More explicit
Independent variable: length from pivot to the centre of mass of the bob, 0.20 to 1.00 m in 0.10 m steps, measured with a metre rule (±0.002 m). Dependent variable: period T, from the time for 20 oscillations to reduce reaction-time error. Controlled: amplitude under 10° (small-angle approximation), same bob mass, rigid clamp. Five repeats per length.
How does the example make data analysis evidence more explicit? (6-mark criterion)
The data is linearised using theory, a physical constant is extracted, and the intercept is used as a check.
Under-specified
The graph shows that longer strings give longer periods.
More explicit
T² was plotted against L to linearise T = 2π√(L/g). The gradient is 4.03 ± 0.09 s² m⁻¹, giving g = 4π²/gradient = 9.80 ± 0.22 m s⁻². The intercept (0.004 s²) is within its uncertainty of zero, consistent with no systematic length error.
How does the example make conclusion evidence more explicit? (6-mark criterion)
It compares with the accepted value using the uncertainty, instead of claiming proof.
Under-specified
The experiment proves the formula is correct and g is 9.8.
More explicit
The linear T² against L relationship supports T = 2π√(L/g) for amplitudes under 10°. The measured g = 9.80 ± 0.22 m s⁻² agrees with the accepted 9.81 m s⁻² within uncertainty (0.1% difference), so no significant systematic error is evident.
How does the example make evaluation evidence more explicit? (6-mark criterion)
Uncertainties are ranked by their effect on specific results, with targeted fixes.
Under-specified
There was air resistance and human error.
More explicit
The largest random error was starting and stopping the timer; a light gate at the lowest point would reduce it. Measuring to the bob's centre of mass was uncertain by about 3 mm, which matters most at 0.20 m. Air resistance would slightly damp the motion but had no visible effect over 20 oscillations.
How do you evaluate each criterion?
Compare the strength and relevance of evidence, reasoning, and evaluation against the criterion's mark-band descriptors.
- Plotting T against L and stopping at a curve.
- Timing single oscillations.
- Ignoring the small-angle condition.
- Claiming the formula is 'proved'.
- Going past the 3,000-word maximum.
Where can you find official IB Physics IA exemplars?
Marked Physics exemplars are in the IB Programme Resource Centre through your school. Ask your teacher for the exemplars that match the first-assessment-2025 criteria.
Sources & verification
Primary-source references used to verify key assessment facts on this page. Last source check: September 24, 2026.
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