MYP · 10 · extended response
Energy and acceleration in an oscillator
Sound and oscillation · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 2
- Answer
- Complete
Restoring force
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Force / N
Horizontal axis (x): Displacement / m
Read the exact data as a table
| Displacement / m | Force / N |
|---|---|
| -0.1 | 2 |
| -0.05 | 1 |
| 0 | 0 |
| 0.05 | -1 |
| 0.1 | -2 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A 0.50 kg glider on a spring performs small, undamped oscillations. Its restoring-force measurements are supplied. At release it is 0.10 m from equilibrium and momentarily at rest. Take the equilibrium displacement as x = 0. Supplied model: Use a = −ω²x, T = 2π/ω, vmax = ωA and v² = ω²(A²−x²). Supplied data (Displacement / m; Force / N): (-0.1, 2), (-0.05, 1), (0, 0), (0.05, -1), (0.1, -2).
- (a)
Show that the force model produces SHM. Find angular frequency, period and maximum speed.
3 marks - (b)
Find speed and acceleration at x = +0.060 m. Explain how damping changes a resonance experiment.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Show that the force model produces SHM. Find angular frequency, period and maximum speed.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
The graph gives F = −20x, so a = F/m = −40x: acceleration is proportional to displacement and directed toward equilibrium.
- 2
Comparing a = −ω²x gives ω = √40 rad s⁻¹ and T = 2π/ω ≈0.993 s.
- 3
The amplitude is 0.10 m. From energy conservation or vmax = ωA, the maximum speed is 0.632 m s⁻¹ at equilibrium.
(b)
Find speed and acceleration at x = +0.060 m. Explain how damping changes a resonance experiment.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
At x = 0.060 m, acceleration is −40(0.060) = −2.4 m s⁻², toward equilibrium.
- 2
Energy gives v² = ω²(A²−x²) = 40(0.0100−0.0036) = 0.256; speed is √0.256 ≈0.506 m s⁻¹, with direction depending on the motion phase.
- 3
A driving frequency near the natural frequency can produce a large response. Damping transfers mechanical energy to the surroundings and reduces and broadens the resonance peak, useful when large vibrations would cause damage.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- The graph gives F = −20x, so a = F/m = −40x: acceleration is proportional to displacement and directed toward equilibrium.
- Comparing a = −ω²x gives ω = √40 rad s⁻¹ and T = 2π/ω ≈0.993 s.
- The amplitude is 0.10 m. From energy conservation or vmax = ωA, the maximum speed is 0.632 m s⁻¹ at equilibrium.
- At x = 0.060 m, acceleration is −40(0.060) = −2.4 m s⁻², toward equilibrium.
- Energy gives v² = ω²(A²−x²) = 40(0.0100−0.0036) = 0.256; speed is √0.256 ≈0.506 m s⁻¹, with direction depending on the motion phase.
- A driving frequency near the natural frequency can produce a large response. Damping transfers mechanical energy to the surroundings and reduces and broadens the resonance peak, useful when large vibrations would cause damage.
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