Nontrivial period annuli in the second order ordinary differential equation are continua of periodic trajectories that contain inside more than one critical point. They can appear in conservative equations, which are known to have no attractors. Nevertheless, according to some authors, their behavior may be done chaotic by adding a periodic external force. Is the period of the external force correlated with periods of solutions in period annuli? Is the chaotic behavior of a solution dependent on the initial value and, in turn, on a certain periodic annulus? These, and related questions are studied in the article.