This paper deals with the nonlinear oscillation of a simple pendulum and presents not only the exact formula for the period but also the exact expression of the angular displacement as a function of the time, the amplitude of oscillations and the angular frequency for small oscillations. This angular displacement is written in terms of the Jacobi elliptic function sn(u;m) using the following initial conditions: the initial angular displacement is different from zero while the initial angular velocity is zero. The angular displacements are plotted using Mathematica, an available symbolic computer program that allows us to plot easily the function obtained. As we will see, even for amplitudes as high as 0.75π (135• ) it is possible to use the expression for the angular displacement, but considering the exact expression for the angular frequency ω in terms of the complete elliptic integral of the first kind. We can conclude that for amplitudes lower than 135 o the periodic motion exhibited by a simple pendulum is practically harmonic but its oscillations are not isochronous (the period is a function of the initial amplitude). We believe that present study may be a suitable and fruitful exercise for teaching and better understanding the behavior of the nonlinear pendulum in advanced undergraduate courses on classical mechanics. Keywords: simple pendulum, large-angle period, angular displacement.Este artigo aborda a oscilação não-linear de um pêndulo simples e apresenta não apenas a fórmula exata do período mas também a dependencia temporal do deslocamento angular para amplitudes das oscilações e a freqüência angular para pequenas oscilações. O deslocamento angularé escrito em termos da função elíptica de Jacobi sn(u;m) usando as seguintes condições iniciais: o deslocamento angular inicialé diferente de zero enquanto que a velocidade angular inicialé zero. Os deslocamentos angulares são plotados usando Mathematica, um disponível programa simbólico de computador que nos permite plotar facilmente a função obtida. Como veremos, mesmo para amplitudes tão grandes quanto 0,75π (135 o )é possível usar a expressão para o deslocamento angular mas considerando a expressão exata para a freqüência angular w em termos da integral elíptica completa de primeira espécie. Concluímos que, para amplitudes menores que 135 o , o movimento periódico exibido por um pêndulo simplesé praticamente harmônico, mas suas oscilações não são isócronas (o períodoé uma função da amplitude inicial). Acreditamos que o presente estudo possa tornar-se um exercício conveniente e frutífero para o ensino e para uma melhor compreensão do pêndulo não-linear em cursos avançados de mecânica clássica na graduação. Palavras-chave: pêndulo simples, período a grandesângulos, deslocamento angular.Perhaps one of the nonlinear systems most studied and analyzed is the simple pendulum [1][2][3][4][5][6][7][8][9][10][11][12], which is the most popular textbook example of a nonlinear system and is studied not only in advanced but also in introductory university courses of...

The Trifid nebula is a young (10(5) years) galactic HII region where several protostellar sources have been detected with the infrared space observatory. The sources are massive (17 to 60 solar masses) and are associated with molecular gas condensations at the edges or inside the nebula. They appear to be in an early evolutionary stage and may represent the most recent generation of stars in the Trifid. These sources range from dense, apparently still inactive cores to more evolved sources, undergoing violent mass ejection episodes, including a source that powers an optical jet. These observations suggest that the protostellar sources may have evolved by induced star formation in the Trifid nebula.