In this paper, the performance of a bat searching algorithm is studied from system dynamics point of view. Bat searching algorithm (BA) is a recently developed swarm intelligence based optimization algorithm which has shown great success when solving complicated optimization problems. Each bat in the BA has two main states: velocity and position. The position represents the solution of the optimization problems while the velocity represents the searching direction and step size during each iteration. Due to the nature of the update equations, the dynamics of the bats are formulated as a group of second-order discrete-time systems. In this paper, the performance of the algorithm is analyzed based on the nature of the responses in the second-order systems. The over-damped response, under-damped responses are studied and the parameters requirements are derived. Moreover, unstable scenarios of the bats are also considered when examining the performance of the algorithm. Numerical evaluations are conducted to test different choices of the parameters in the BA.