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A2 Daily A Level Physics question

2026-01-24 OCR A Simple Harmonic Motion (M5.1) 3.4.2 Materials: Springs in series and parallel (effective spring constant) 5.1.1 Simple harmonic motion: period dependence on mass and stiffness (mass–spring system)

In a lab, a student times vertical oscillations of a mass on a spring. She then doubles the mass and, at the same time, adds a second identical spring in parallel so both springs share the load. Assuming small oscillations and negligible damping, what happens to the period of oscillation and why?

  1. A It stays the same; doubling the mass and adding an identical spring in parallel (doubling stiffness) have equal and opposite effects on the period. (correct)
  2. B It doubles; extra mass makes oscillations slower even if more springs are used.
  3. C It halves; two springs in parallel make the system twice as stiff, so it oscillates twice as fast.
  4. D It increases by about 40%; the mass increase has a larger effect than the added stiffness.

Answer

The correct answer is A.

Correct: A — It stays the same; doubling the mass and adding an identical spring in parallel (doubling stiffness) have equal and opposite effects on the period. Using the dependence on the square root of mass over stiffness, T2/T1 = sqrt[(2m/2k)/(m/k)] = 1, so the period is unchanged. B is wrong because increasing mass alone would increase the period, but here the doubled stiffness offsets it exactly. C is wrong because doubling stiffness alone would reduce the period by a factor of 1/√2, not by 1/2, and in any case the simultaneous mass doubling cancels the change. D is wrong because the effects are equal in magnitude when both mass and stiffness are doubled; there is no net 40% increase.

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