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We study dynamics of two coupled periodically driven oscillators. Importantexample of such a system is a dynamic vibration absorber which consists of asmall mass attached to the primary vibrating system of a large mass.  Periodic solutions of the approximate effective equation are determinedwithin the Krylov-Bogoliubov-Mitropolsky approach to get the amplitude profiles$AOmega) $.  Dependence of the amplitude $A$ of nonlinear resonances on the frequency $\Omega $ is much more complicated than in the case of one Duffing oscillatorand hence new nonlinear phenomena are possible. In the present paper we studymetamorphoses of the function $A(\Omega) $ induced by changes of the controlparameters.

Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation