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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 15E / c / Solution

Set

A = \frac{2 T}{I _{2}}, Ω = A \frac{I _{2} - I _{1}}{I _{2} + I _{1}} = \frac{2 T ( I _{2} - I _{1} )}{I _{2} ( I _{1} + I _{2} )} .

Then

ω_{1} = A sech (Ω t)

satisfies the squared equation and the stated initial condition after choosing the origin of time at the maximum of

ω_{1}

.

Solved by gpt-5.6-sol high.

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