  A sheet of elastic foil rolled into a cylinder and deformed between two
parallel plates acts as a non-Hookean spring if deformed normally to the axis.
For large deformations the elastic force shows an interesting inverse squares
dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699
(2010)]. The phenomenon has been used as a basis for an experimental problem at
the 41st International Physics Olympiad. We show that the corresponding
variational problem for the equilibrium energy of the deformed cylinder is
equivalent to a minimum action description of a simple gravitational pendulum
with an amplitude of 90 degrees. We use this analogy to show that the power-law
of the force is exact for distances less than a critical value. An analytical
solution for the elastic force is found and confirmed by measurements over a
range of deformations covering both linear and non-Hookean behavior.
