The Earth's free core nutation: Formulation of dynamics and estimation of eigenperiod from the very-long-baseline interferometry data

•We formulate the excitation dynamics of Earth's free-core nutation.•The temporal convolution well explains the behavior of FCN observed in VLBI data.•The deconvolution formulism leads to optimum estimates for FCN's eigenperiod P from VLBI data.•Our optimum estimate is P=441±4.5sd, lying between the theoretical value and past estimates.