 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-4/16c/b/iv/solution

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

With

Z^{'} (0) = k

, the linearized kinematic condition gives

cos \frac{π x}{L} cos \frac{2 π y}{L} H^{'} (t) = k cos \frac{π x}{L} cos \frac{2 π y}{L} F (t) .

Hence

η (x, y, t) = cos \frac{π x}{L} cos \frac{2 π y}{L} H (t), H^{'} (t) = k F (t) .

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