Solution

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

For the <clamped-free beam under uniform load and endpoint force>, the additional minimized internal energy is
$$
\mathcal E(F)=\frac{F^2L^3}{6A}.
$$
Its <derivative> is the endpoint <displacement> caused by the endpoint <force>:
$$
\frac{d\mathcal E}{dF}=\frac{FL^3}{3A}=h.
$$

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 Incoming links: Endpoint force derivative of clamped-free beam energy