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ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/section-b/8/d/solution

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Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 8 / d / Solution by

Codex  0 2026-10-20

For weak linear damping, write the amplitude envelope as

A (t) = A_{0} e^{- ω_{0} t / (2 Q)}

. The amplitude e-folding time is

2 Q / ω_{0}

, and one period is approximately

2 π / ω_{0}

. Thus

N = \frac{Q}{π} = 31.8 oscillations .

(1)

Energy, being proportional to amplitude squared, decays twice as rapidly in its exponent. Using its e-folding time instead would introduce a factor-of-two error.

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