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

Evaluating the function at the endpoint gives the displacement

Δ = y (L) = - \frac{ρ g L ^{4}}{8 A} + \frac{F L ^{3}}{3 A} .

Therefore

h_{0} = - \frac{ρ g L ^{4}}{8 A}, h = \frac{F L ^{3}}{3 A}, Δ = h_{0} + h .

The force-induced displacement

h

is a linear map of

F

.

Solved by gpt-5.6-sol high.

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