= Diameter-rod oscillation in cylindrical gravity
{title2=$\omega^2=2\pi G\rho$}
A thin rod of length $2R$ and <linear mass density> $\lambda$ slides along a diameter of an infinite uniform source cylinder of radius $R$. Neglect the narrow hole's perturbation of the source field. If the rod centre is displaced by $x$, $F(x)=\lambda\int_{x-R}^{x+R}g_y(y)\,dy$. The endpoint derivative gives $F'(0)=\lambda[g_y(R)-g_y(-R)]=-4\pi G\rho\lambda R$. Dividing the restoring coefficient by rod <mass> $2R\lambda$ gives the displayed small-oscillation <frequency>.
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