This note is an addendum to the results of P. O. Frederickson and A. C. Lazer [J. Differential Equations 5 (1969), 262–270; MR0234061], and Lazer [in Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables, FL, 1999), 113–119, Electron. J. Differ. Equ. Conf., 5, Southwest Texas State Univ., San Marcos, TX, 2000; MR1799049] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [A. C. Lazer, op. cit.] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem.