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A2 Daily A Level Physics question

2026-03-27 OCR A SHM, damping and resonance bandwidth (M5) Module 5.1.3 Simple harmonic motion: measurement of period and frequency Module 5.1.4 Damping and resonance (qualitative): resonance curves, bandwidth and energy dissipation Practical skills: extracting half-power bandwidth from amplitude–frequency data

In a lab, a mass–spring system is driven by a shaker providing a sinusoidal force of fixed amplitude. With light damping, the resonance peak occurs at f0 = 2.0 Hz, and the two half-power frequencies are measured as 1.8 Hz and 2.2 Hz. A second identical damping vane is then added so that the resistive (drag) coefficient doubles; the shaker force amplitude is unchanged. Which outcome is most consistent with this change?

  1. A Peak amplitude halves; the half-power width Δf falls to about 0.2 Hz; the peak frequency rises noticeably.
  2. B Peak amplitude doubles; the half-power width Δf grows to about 0.8 Hz; the peak frequency stays the same.
  3. C Peak amplitude halves; the half-power width Δf grows to about 0.8 Hz; the peak frequency is almost unchanged. (correct)
  4. D Peak amplitude is essentially unchanged; the half-power width Δf stays near 0.4 Hz; the peak frequency shifts down a lot.

Answer

The correct answer is C.

Correct: C — Peak amplitude halves; the half-power width Δf grows to about 0.8 Hz; the peak frequency is almost unchanged. Doubling the damping (energy dissipated per cycle) reduces the resonant amplitude roughly in inverse proportion, and broadens the resonance; the initial half-power width is 2.2−1.8 = 0.4 Hz, so doubling damping gives Δf ≈ 0.8 Hz, while the peak frequency shifts only slightly for light damping. A … Increased damping does not narrow the resonance; it broadens it, and the peak frequency does not rise noticeably (it tends to drop slightly, if at all). B … The amplitude does not increase when damping is increased; it decreases, though the doubling of Δf is correct and the peak frequency changes little. C … Matches the expected inverse effect on peak amplitude and proportional increase in bandwidth, with only a small change in peak frequency. D … Damping affects both amplitude and bandwidth; leaving them unchanged while claiming a large downward shift in peak frequency contradicts the behaviour of a lightly damped driven oscillator.

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