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We consider the effects of magnetostatic interaction and ferromagnetic resonance in a frustrated system of anisotropic ferromagnetic nanoparticles packed in a two-dimensional lattice with hexagonal symmetry (artificial spin ice). It is demonstrated, that in an array of interacting particles there are two stable states with a quasi-homogeneous magnetic moments configuration and with a zero magnetic moment. It is shown that the spectrum of ferromagnetic resonance in such system strongly depends on the degree of interaction and the spatial configuration of the magnetic moments. [ABSTRACT FROM PUBLISHER]