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ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2024/paper-3/8/c/ii/solution

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Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2024 / Paper 3 / 8 / c / ii / Solution by

Codex  0 2026-10-25

x = 10 δ_{D}

, the daily component is multiplied by

e^{- 10} ≃ 4.54 \times 1 0^{- 5}

and has a lag of ten radians. The annual component instead has

x / δ_{Y} = 10/ 365 ≃ 0.5234

. Hence

Θ - Θ_{0} = A e^{- 10/ 365} cos (ω_{Y} t - 10/ 365) + B e^{- 10} cos (ω_{D} t - 10) .

(1)

The sketch is nearly a smooth annual sinusoid, with annual amplitude about $0.5925 A$ and annual phase lag about $0.5234$ radians, corresponding to about

30.4

days on the chosen year scale. The tiny daily component is retained in the formula rather than declared identically zero.

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