= Electrostatic softening above a conducting wedge
{title2=$\omega_y^2=(k-2\beta/y_e^3)/m$}
For an attractive <force> $-\beta/y^2$ and an otherwise linear vertical <spring>, differentiation about the charged <equilibrium> $y_e$ reduces the <spring> stiffness by $2\beta/y_e^3$. If the uncharged height is $y_0$ and the shift is small, the fractional <frequency> change is $-\beta/(ky_0^3)$. Using only the <force> value, without its <derivative>, would miss this <frequency> shift.
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