= Tip-force compliance of a cantilever
{title2=$h(L)/f=L^3/(3A)$}
For a clamped <elastic filament> of <filament bending modulus> $A$, a transverse tip force $f$ gives $h(x)=fx^2(3L-x)/(6A)$ in the small-slope model. Thus $h(L)/f=L^3/(3A)$. This differs from the effective tip stiffness under a distributed load. The zero-load Gaussian response reproduces the <thermal bending fluctuations of a clamped filament>, $\langle h(L)^2\rangle=k_BTL^3/(3A)$ for one transverse coordinate.
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