  We solve analytically the Langevin dynamics of the classic spherical model
considering the ferromagnetic exchange and a long-range antiferromagnetic
interaction. Our results in the asymptotic regime, shows an equivalence in the
functionality of the spatial and self-correlations between this model and the
recently studied Ginzburg-Landau frustrated model within the Hartree
approximation. A careful discussion is done about the low temperature behavior
in the context of glassy dynamics. The appearance of interesting features
regarding the establishment of the ferromagnetic phase is also analyzed in view
of the effects of the spherical restriction. We propose a new variant of the
spherical model in which the global restriction is substituted by an infinite
set of restrictions over finite size regions. This modification leads to a new
dynamical equation that suggests the appearance of the low temperature phase
transition even in the non-frustrated case were the classic spherical model
fails.
