The idea of resonant spin oscillation method was modernized and improved in Forschungszentrum Jülich in the proposed experiment at the COSY ring. The resonant method is based on spin tune parameterization using transverse RF magnetic or/and electric field. The spin orientation smearing due to the finite spin coherence time (SCT) plays a crucial role in the proposed experiment to search for the electric dipole moment. Our analysis is based on the T-BMT differential equations for spin together with shorten motion equations. Using well developed theory of Mathieu's differential equations we have got simplified analytic solution for prediction of spin behaviour. In this paper we have numerically evaluated all effects having fundamental contributions.