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Rubber bands are another good non-Hookeish spring with characteristics
similar to car springs. I once studied their curve for purposes of
designing a "banana car" for a local science museum competition. The
purpose was to build a rubber band powered device (we call them
"elastic bands" here in Canada) which, using two standard rubber bands,
could carry a banana the greatest distance over a flat track within a
prescribed width. It was worthwhile to take account of the non-Hookeish
characteristic.
Leigh