 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2/7c/a/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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}

I

t_{0}

, as required.

 New to topics? Read the docs here!