A discussion on approximations for the determination of the maximum   period of a simple pendulum
  In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's surface. 
Rog\'erio Netto Suave and Jos\'e Alexandre Nogueira
physics.class-ph