Cambridge International A-Level Physics · topic 17
Oscillations
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
Energy and acceleration in an oscillator
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]
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.
Show a hint
Begin with part (a): Show that the force model produces SHM. Find angular frequency, period and maximum speed.
Reveal the worked solution
- 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.
Answer (a) ω = √40 ≈6.32 rad s⁻¹; T ≈0.993 s; vmax ≈0.632 m s⁻¹. (b) Speed magnitude ≈0.506 m s⁻¹; acceleration = −2.4 m s⁻².
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.