  This paper presents the theory and key experimental findings for an
investigation into the generation of bimodal resonance (frequency splitting)
phenomena in mutually over-coupled inductive sensors, and its exploitation to
evaluate relative separation and angular displacement between coils. This
innovative measurement technique explores the bimodal resonant phenomena
observed between two coil designs - solenoid and planar coil geometries. The
proposed sensors are evaluated against first-order analytical functions and
finite element models, before experimentally validating the predicted
phenomenon for the different sensor configurations. The simulated and
experimental results show excellent agreement and first-order best-fit
functions are employed to predict displacement variables experimentally.
Co-planar separation and angular displacement are shown to be experimentally
predictable to within $\pm1mm$ and $\pm1^o$ using this approach. This study
validates the first-order physics-based models employed, and demonstrates the
first proof-of-principle for using resonant phenomena in inductive array
sensors for evaluating relative displacement between array elements.
