Exchange of dominance between twin kHz quasi-periodic oscillations (QPOs) observed in some low-mass-X-ray-binaries (LMXBs) suggests the possibility of a resonance between two oscillatory modes. We study the behaviour of the effective gravitational potential around specific resonant radii, and estimate the role of the higher-order terms governing the non-linear, anharmonic forcing. We discuss the impact it has on the mode amplitude in the linear and non-linear regimes. We also discuss a related possibility of lowering of the neutron star mass estimates from the highest observed QPO frequencies.