In this paper,we study the existence of nontrivial periodic solutions for second order dynamical systems x+k²x=f(t,x)+e(t), here 0<k<π/T and f∈C((R/TZ)×R^N\{0},R^N) has a repulsive singularity at the origin.We do not need any coercivity conditions,therefore we can deal with the case of a strong singularity as well as the case of a weak singularity.The proof is based on a nonlinear alternative principle of Leray-Schauder.