Inverse Design from the Catenary Problem

Inverse problems in science normally involve the challenge of obtaining from a set of observations the causal factors that generated them in the first place. However, physics students are seldom exposed to such problems as part of their training. Here we revisit the mechanics problem of finding the shape of a hanging cable, but this time in reverse, {\it i.e.}, by asking what mass density a cable must have to follow a specific shape. This concept is then generalised into the possibility of identifying a cable whose hanging shape follows any form we wish to design. This inverted design strategy is experimentally verified with an inexpensive setup that is suitable for classroom activities.