  Topological properties of solid states have sparked considerable recent
interest due to their importance in the physics of lattices with a non-trivial
basis and their potential in the design of novel materials. Here we describe an
experimental and an accompanying numerical toolbox to create and analyze
topological states in coupled radiofrequency resonator arrays. The arrays are
coupled harmonic oscillator systems that are very easily constructed, offer a
variety of geometric configurations, and whose eigenfunctions and eigenvalues
are amenable to detailed analysis. These systems offer well defined analogs to
coupled oscillator systems in general in that they are characterized by
resonances whose frequency spectra depend on the individual resonators, the
interactions between them, and the geometric and topological symmetries and
boundary conditions. In particular, we describe an experimental analog of a
small one-dimensional system, with excellent agreement with theory. The
numerical part of the toolbox allows for simulations of larger mesoscopic
systems with a semi-continuous band structure, in which all resonators still
exhibit individual signatures. Systematic parameter variation yields an
astonishing richness of band structures in this simple linear system, allowing
for further explorations into novel phenomena of topological modes.
