This study revisits the sampled-data consensus algorithm for agents modelled by double-integrator dynamics under both fixed and dynamic network topology. Totally different methods are employed to perform the convergence analysis. Under certain assumptions on the sampling period and the velocity damping gain, a necessary and sufficient condition is given for the agents under fixed network topology to reach consensus. In addition, the method employed in performing the convergence analysis for the fixed case can be further extended to achieve a similar result as that in the existing literature for the dynamical case in a more general setting. The consensus equilibria are also analysed for the system evolving under a special class of dynamic network topology.