AP · AP C:M · multiple choice
AP Physics C: Mechanics · Question 6
AP Physics C: Mechanics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 1
- Topics
- 1
- Answer
- Complete
A particle of mass m moves in a potential U(x) = ½kx⁴. Which statement about its motion for small oscillations about x = 0 is correct?
- A
The motion is simple harmonic with angular frequency √(k/m).
- B
The motion is simple harmonic with angular frequency √(2k/m).
- C
The motion is periodic but not simple harmonic, and its period depends on the amplitude.
- D
The motion is not periodic.
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Answer and reasoning
Predict from the governing principle before looking for a matching option. Then reject alternatives by checking direction, units, limiting behaviour or the physical meaning of each statement.
- 1
The correct choice is C: The motion is periodic but not simple harmonic, and its period depends on the amplitude.
- 2
The restoring force is −dU/dx = −2kx³, which is not proportional to x, so the motion cannot be simple harmonic however small the amplitude. A and B are offered to candidates who assume any potential minimum gives SHM.
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