IB · C · data analysis
Wave behaviour · Question 7
Wave behaviour · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 11
- Topics
- 1
- Answer
- Complete
A student investigates the oscillations of a mass hanging from a vertical spring, expecting the period to satisfy T = 2π√(m/k), where k is the spring constant.
| m / kg | 0.100 | 0.200 | 0.300 | 0.400 | 0.500 |
|---|---|---|---|---|---|
| T / s | 0.444 | 0.628 | 0.770 | 0.889 | 0.993 |
| T² / s² | 0.197 | 0.395 | 0.592 | 0.790 | 0.987 |
- (a)
Determine Determine the gradient of a graph of T² against m, and hence determine the spring constant k.
4 marks - (b)
Explain Explain why the student plotted T² against m rather than T against m.
2 marks - (c)
Suggest In practice the line of best fit for a real spring has a small positive intercept on the T² axis. Suggest a physical reason for this.
2 marks - (d)
Outline Outline how the student should time the oscillations to keep the uncertainty in T small, and state one reason why timing a single oscillation would be unsatisfactory.
3 marks
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(a)
Determine Determine the gradient of a graph of T² against m, and hence determine the spring constant k.
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
T² = (4π²/k)m, so the gradient is 4π²/k
- 2
gradient = (0.987 − 0.197)/(0.500 − 0.100) = 0.790/0.400
- 3
gradient = 1.98 s² kg⁻¹
- 4
k = 4π²/1.98 = 20 N m⁻¹
(b)
Explain Explain why the student plotted T² against m rather than T against m.
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
T against m would be a curve, from which no constant can be read directly
- 2
squaring produces a linear relationship, so a straight line both tests the model and gives k from a single gradient
(c)
Suggest In practice the line of best fit for a real spring has a small positive intercept on the T² axis. Suggest a physical reason for this.
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
the spring itself has mass, and part of it oscillates along with the hanging mass
- 2
so the effective oscillating mass exceeds the mass added, giving a non-zero period as the added mass tends to zero — the intercept corresponds to roughly one third of the spring's own mass
(d)
Outline Outline how the student should time the oscillations to keep the uncertainty in T small, and state one reason why timing a single oscillation would be unsatisfactory.
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
time at least 10 or 20 complete oscillations and divide by the number
- 2
start and stop the timing as the mass passes through the equilibrium position, where it moves fastest, using a fixed reference marker
- 3
the reaction-time uncertainty of about 0.2 s is a large fraction of a single period of about 0.5 s, but only a small fraction of a 10-oscillation total
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