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Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 4 / 11B / b / Solution

Along

BC

, write

x = (2 a, s, 0)

. With

ω = - α \overset{z}{^} / t

, the tangential equation is

\overset{s}{¨} = \frac{α ^{2} s - 2 a α}{t ^{2}} .

A stationary point is

s_{0} = 2 a / α

, lying on the side iff

α \geq 1

. The general perturbed motion is

s = s_{0} + C t^{(1 + 1 + 4 α^{2}) /2} + D t^{(1 - 1 + 4 α^{2}) /2} .

Except on the decaying-mode fine tuning, the growing term carries the bead to

B

or

C

, according to its sign.

Solved by gpt-5.6-sol high.

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