 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/33b/c/solution

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

For small

μ

\dot{H}

around

x = r cos 2 t

y = - r sin 2 t

. This gives

⟨ \dot{H} ⟩ = μ [r^{2} - (3 a + 1) r^{4} /4]

. The unique positive balance is

r = 2/ 3 a + 1

, which lies between

1/ a

and

1

for

a > 1

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