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Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 7C / a / iii / Solution

Put

T = π / ω

,

t_{0} = T /2

, and

Ω = ω /2

. A solution satisfying both endpoint conditions is

y = A e^{- γ t /2} sin (Ω t) + \frac{I}{Ω} e^{- γ (t - t_{0}) /2} sin (Ω (t - t_{0})) H (t - t_{0}),

where

A = - 2 I ω^{- 1} e^{3 π /4}

. The derivative jumps by

I

at

t_{0}

, as required.

Solved by gpt-5.6-sol high.

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