In this article, we propose to use van Vleck's contact transformation method for the study of time-dependent interactions in solid state nuclear magnetic resonance (NMR) by Floquet theory [A. Schmidt and S. Vega, J. Chem. Phys. 96, 2655 (1992)]. Floquet theory has been used for studying the spin dynamics of magic angle spinning (MAS) NMR experiments. The contact transformation method is an operator method in time-independent perturbation theory and has been used to obtain effective Hamiltonians in molecular spectroscopy. Here the above method is combined with Floquet theory to study the dynamics of a dipolar coupled spin (I=1/2) system. In order to determine the frequencies and intensities of bands in MAS spectra, we need to diagonalize the Floquet-Hamiltonian matrix. This is generally done numerically, by truncating the infinite dimensional Floquet-Hamiltonian matrix. Here we propose an effective Floquet-Hamiltonian for the system. We demonstrate the application of the above method to a homonuclear dipolar coupled spin system (I=1/2). The eigenvalues obtained from the above are compared with those obtained using numerical diagonalization. The eigenvalues of the effective Hamiltonian compare quite well with those computed using numerical diagonalization of Floquet matrices.