  We consider the mass-in-mass (MiM) lattice when the internal resonators are
very small. When there are no internal resonators the lattice reduces to a
standard Fermi-Pasta-Ulam-Tsingou (FPUT) system. We show that the solution of
the MiM system, with suitable initial data, shadows the FPUT system for long
periods of time. Using some classical oscillatory integral estimates we can
conclude that the error of the approximation is (in some settings) higher than
one may expect.
