This technical note studies the synchronization of discretely coupled harmonic oscillators by using an impulsive control strategy. In the absence of velocity measurements, a distributed protocol for the coupled harmonic oscillators is proposed under the assumption that each oscillator can only obtain the information of its position relative to its neighbors at a series of discrete time moments. Necessary and sufficient conditions are established for the synchronization of the networked system with and without an active leader over an undirected communication topology. The desirable sampling period is analytically found to be dependent on the network topology and position gain. A simple iterative method is developed to calculate the range in which the sampling period falls. Finally, numerical simulations are performed to show the effectiveness of the proposed protocols.