 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-4/16b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

\overset{x}{¨} + ω^{2} x = 0

and

\overset{y}{¨} + ω^{2} y = 0

. They imply

\dot{J} = \overset{x}{¨} y - \overset{y}{¨} x = 0.

x = A cos ω t + B sin ω t, y = C cos ω t + D sin ω t,

gives the conserved value

J = ω (BC - A D) .

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