 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-2/5c/b/solution

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

x (s) = (x (s), y (s), z (s))

satisfies

\overset{x}{˙} = α y, \overset{y}{˙} = - αx, \overset{z}{˙} = β,

with

(x (0), y (0), z (0)) = (1, 0, 0)

. Therefore

x (s) = cos (α s), y (s) = - sin (α s), z (s) = β s .

For

β \neq = 0

this is a helix, with

x = cos (α z / β)

and

y = - sin (α z / β)

; for

β = 0

it is the unit circle in the plane

z = 0

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