We investigate the dynamics of a copolymer molecule in a theta -solvent under a weak alternating field using the Zimm model. We first consider a diblock copolymer with two blocks of same force constant, where the monomers on the two different blocks interact with the applied field differently. The theory predicts that the center-of-mass and the chain conformation of copolymer molecules oscillate in response to the sinusoidal electric field. For the center-of-mass, the oscillation becomes more pronounced as the charge fraction is increased. However, the oscillation of chain conformation is not observed for neutral or fully charged homopolymers, but is enhanced when the fraction of the two blocks becomes equal. In highly viscous solutions, the strength of the oscillation of the center-of-mass and conformation is weakened, and the phase of oscillation is shifted. Moreover, the oscillatory behavior diminishes at higher frequencies. For comparison, we also study a special copolymer model where the two monomers alternate along the polymer backbone. Again the oscillation emerges for the molecular motion and conformation, but the oscillation of chain properties becomes much weaker than diblock copolymers. These results disclose the effect of the chemical architectures of copolymers on their chain dynamic behavior under an alternating field.