The problem of reactivity oscillations for a point reactor constitutes an interesting aspect of nuclear reactor physics and its solution may give important information for dynamic and safety assessments. The present paper considers the problem of a reactivity oscillation for a source-driven system which involves some specific aspects that introduce significant differences with respect to the source-free situation. Assuming a square-wave shape for the reactivity insertion, the solution is derived by a fully analytical approach. The conditions for stability and instability can be identified in a straightforward way by directly studying the stationarity of the power response. Numerical results presented allow to discuss the role of the system kinetic parameters and of the time-shape of the reactivity wave.