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The authors are concerned with consensus problems in undirected networks of multiple agents with second-order dynamics, where each agent can only obtain the measurements of its positions relative to its neighbours at sampling instants. A new protocol based on sampled-data control is proposed so that all agents can reach consensus on their positions and velocities, respectively. Both fixed and switching topology cases are considered. For the fixed topology case, a sufficient and necessary condition for consensus is derived in the case without time delays, and an allowable upper bound of time delays is obtained in the case with time delays. For the switching topology case, sufficient conditions are established for consensus under arbitrary switching signals and under a class of switching signals, respectively. Simulations are provided to illustrate the effectiveness of the theoretical results.