  We examine the focusing of kinetic energy and the amplification of various
quantities during the snapping motion of the free end of a flexible structure.
This brief but violent event appears to be a regularized finite-time
singularity, with remarkably large spikes in velocity, acceleration, and
tension easily induced by generic initial and boundary conditions. A numerical
scheme for the inextensible string equations is validated against available
experimental data for a falling chain and further employed to explore the
phenomenon. We determine that the discretization of the equations, equivalent
to the physically discrete problem of a chain, does not provide the
regularizing length scale, which in the absence of other physical effects must
then arise from the geometry of the problem. An analytical solution for a
geometrically singular limit, a falling perfectly-folded string, accounts
surprisingly well for the scalings of several quantities in the numerics, but
can only indirectly suggest a behavior for the curvature, one which seems to
explain prior experimental data but does not correspond to the evolution of the
curvature peak in our system, which instead displays a newly observed
anomalously slow scaling. A simple model, incorporating only knowledge of the
initial conditions along with the anomalous and singular-limit scalings,
provides reasonable estimates for the amplifications of relevant quantities.
This is a first step to predict and harness arbitrarily large energy focusing
in structures, with a practical limit set only by length scales present in the
discrete mechanical system or the initial conditions.
