1 The non-oscillatory behavior of the pendulum equation K. K. D. Adjaï 1 , A.V. R. Yehossou 1 , J. Akande 1 , M. D. Monsia 1* 1- Department of Physics, University of Abomey-Calavi, Abomey-Calavi, 01.BP.526, Cotonou, BENIN Abstract We study in this work the pendulum equation. We show for the first time the existence of general non-periodic solution for this equation. This comes down to say that the pendulum equation can exhibit non-oscillatory behavior. Keywords: pendulum equation, periodic solution, non-oscillatory behavior, Lienard type equation. Introduction The study of the pendulum began in the time of Huyghens. After the establishment of its differential equation [1-3] 0 sin = + x x β & & (1) where the dot over a symbol means the derivative with respect to time, and β is an arbitrary parameter. The determination of general solution of (1) has been for a long time a challenging problem in mathematics and physics. The general periodic solution of the pendulum equation (1) with an analytical method which does not imply the physical law of energy conservation has been only derived in a recent work performed by Akande and coworkers [2] within the framework of the generalized Sundman transformation theory. The pendulum equation (1) is well known in the literature to have periodic solutions. However, non-periodic solutions have been exhibited for many nonlinear differential equations of Lienard type recently in the literature. In this perspective no one can say whether the equation (1) has non-periodic solution for arbitrary value of 0 > β . The objective in this paper is to show that the pendulum equation can exhibit non- periodic solution. To do so we establish the pendulum equation (1) from the general class of Lienard type equation introduced recently in [4-6] and solve it to calculate the general non-periodic solution (section 2). Finally we perform a conclusion for the work. * Corresponding author : E-mail: monsiadelphin@yahoo.fr