 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-4/11b/b/solution

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

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}} .

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

C

, according to its sign.

 New to topics? Read the docs here!