This paper presents a simple and efficient identification algorithm. The proposed algorithm can be used in a large class of plants whose dynamics can be fairly approximated by an under-damped second-order model. The presented study, determines the minimum time duration of a step pulse input, in order to produce output response, rich enough to generate the model parameters, within accepted accuracy limits. The proposed approach can be applied for on-line estimation, of basic model parameters of an aircraft longitudinal dynamics, during flight. Computer simulation results showed that the proposed simplified technique is capable to determine the unknown model parameters, within acceptable accuracy, and shorter time. Due to easy application, and great reduction of computation time, which is a major problem in most indirect adaptive control algorithms, the proposed scheme can be used for adaptive control of a large class of real plants under actual practical conditions.