The electromagnetic field coupled to a nonlinear medium of having nonvanishing polarizations and magnetizations could be modeled as a classical anharmonic oscillator with velocity- and position-dependent anharmonicities. The Hamiltonian corresponding to the quantum anharmonic oscillator with velocity- and position-dependent anharmonicities is obtained from the knowledge of its classical counterpart. Under rotating wave approximation, the solution of the oscillator with q-dependent and p-dependent anharmonicities exhibit the shifts of the resonance peak frequency. Interestingly, the shifts of the resonance peak of the oscillator due to the q-dependent anharmonicity is opposite to those of the corresponding shifts due to the p-dependent anharmonicity. Therefore, the shifts of the resonance peak frequency asserts the presence of particular anharmonicity as well (i.e. p- or q-type).