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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-2/13c/b/v/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 13C / b / v / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

Taking the derivative of the force-dependent energy gives

\frac{d E}{d F} = \frac{F L ^{3}}{3 A} = h .

(1)

Thus the derivative of the additional minimized internal energy with respect to the applied force equals the resulting endpoint displacement. This is the endpoint force derivative of clamped-free beam energy.

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