Deep in the sugar shock of eating too many Easter "Peeps", I came up with the following:
Consider a bowl formed from the lower half of a sphere. In 2D I can write the equation for the bowl as x^2 + (y-1)^2 = 1.
This gives y = 1 - sqrt(1-x^2)
If I place a marble at the inside rim (x=1, y=1) of the bowl and release it, the marble will oscillate back and forth, repeatedly coming back to the release point.
The potential energy is given by U=mgh=mgy = mg[1 - sqrt(1-x^2)]
Using F_x = - dU/dx , then we have F_x = -x/sqrt(1-x^2) which implies that F_x is infinitely strong when x = 1 (the release point).