We present a simple model to describe the transient response of two coupled resonators probed by a monochromatic wave whose frequency is rapidly swept across the resonances with respect to their characteristic photon lifetimes. The model is applied to analyze the dynamic behaviour of the modal coupling between two degenerate resonances of the same cavity. In particular, this can be used to describe the coupling of counter propagating whispering gallery modes (WGMs) by Rayleigh scattering. The theory is successfully compared to experiments carried out in silica microspheres. These results show that this ringdown technique can be extended to accurately measure linear properties and frequency splittings of high-quality factor WGM micro-resonators.