 Solution

ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2021/paper-ne1/2/d/solution

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Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 2 / d / Solution by

Codex  0 2026-10-20

Multiply the supplied inhour equation by

ω + λ

and collect powers of the inverse period:

Λ ω^{2} + (Λ λ + β - ρ) ω - ρ λ = 0.

With the stipulated constants this becomes

ω^{2} + 12.1 ω - 0.2 = 0,

ω_{+} = 0.0165064 s^{- 1}

and

ω_{-} = - 12.1165 s^{- 1}

. The negative root describes a rapidly decaying component. The positive root governs the late-time growth, giving

T_{+} = ω_{+}^{- 1} = 60.58 s ≃ 60.6 s .

The growing-mode e-folding time is not the precursor mean lifetime, and the negative root is a legitimate transient mode rather than an unphysical negative time.

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