Car springs are an important application of non-Hookeish springs. Leaf
springs are built with varying thickness and width as well as in multi-
leaf bundles. Stops are also sometimes employed. Coil spring are usually
less elegant, but usually have some variation in the pitch of the coil.
This might be a fun experiment for the highschool students. Just pile
cinder blocks in the trunk of a car and measure the deflection of the
springs. Plot F vs x and see what comes out. Find an old Chevy II or
Nova with mono-leaf springs and see if they generate a significantly
different curve than the multi-leaf packs.