MYP Physics · 10 · data analysis
Testing the small-angle pendulum model
Sound and oscillation · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 8
- Topics
- 1
- Answer
- Complete
The same pendulum is released from different angles. A student times ten complete oscillations for each angle.
| Release angle / ° | Time for 10 oscillations / s |
|---|---|
| 5 | 12.6 |
| 10 | 12.6 |
| 20 | 12.7 |
| 30 | 12.9 |
| 40 | 13.4 |
- a
Calculate Calculate the period at 10° and at 40°.
2 marks - b
Evaluate A simple model says the period is independent of amplitude for small angles. Evaluate the data against this model.
3 marks - c
Improve Propose how to decide more confidently where the small-angle approximation ceases to be useful.
3 marks
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a
Calculate Calculate the period at 10° and at 40°.
Read the data before explaining it. Quote the relevant values or trend, show the comparison or calculation, and then connect that numerical evidence to the physical conclusion—including uncertainty or anomalies when they matter.
- 1
Calculates period at 10° = 12.6 ÷ 10 = 1.26 s.
- 2
Calculates period at 40° = 13.4 ÷ 10 = 1.34 s.
b
Evaluate A simple model says the period is independent of amplitude for small angles. Evaluate the data against this model.
Read the data before explaining it. Quote the relevant values or trend, show the comparison or calculation, and then connect that numerical evidence to the physical conclusion—including uncertainty or anomalies when they matter.
- 1
Notes that 5°–20° times are nearly constant at 12.6–12.7 s for ten oscillations.
- 2
Notes a clearer increase at 30° and especially 40°.
- 3
Concludes that the model is supported for the smaller tested angles but becomes less reliable as angle increases.
c
Improve Propose how to decide more confidently where the small-angle approximation ceases to be useful.
Read the data before explaining it. Quote the relevant values or trend, show the comparison or calculation, and then connect that numerical evidence to the physical conclusion—including uncertainty or anomalies when they matter.
- 1
Uses more angle values, especially between 20° and 40°.
- 2
Repeats timings at each angle and calculates means and spread or uncertainty.
- 3
Defines an acceptable difference from the low-angle period before judging the model's useful range.
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