 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/14d/a/solution

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

\overset{q}{˙} = p

and

\overset{p}{˙} = - ω^{2} q

, hence

\overset{q}{¨} + ω^{2} q = 0

I = \frac{1}{2 π} \oint p d q = \frac{1}{2 π} \times π 2 E \frac{2 E}{ω} = \frac{E}{ω} .

Thus

E = ω I

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