In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functions associated with the individual agents and the interaction between agents is described by a weighted undirected graph. We show the exponential convergence of the proposed algorithm if the underlying graph is connected, each private cost function is locally gradient-Lipschitz- continuous, and the global objective function is restricted strongly convex with respect to the global minimizer. Moreover, to reduce the overall need of communication, we then propose a dynamic event-triggered communication mechanism that is free of Zeno behavior. It is shown that the exponential convergence is achieved if the private cost functions are also globally gradient-Lipschitz- continuous. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.