The instability of oscillations of a weightless rod with a concentrated mass, sliding periodically along the rod axis is investigated. This is the simplest model of a child's swing. The amplitude of the displacement of the mass and viscous friction, due to the air resistance, are assumed to small, while the periodic excitation function is arbitrary. Asymptotic formulae for the regions of instability (parametric resonance) in three-dimensional space of the system parameters, corresponding to swinging of the swing, are obtained and investigated. Examples are given.