A complete analysis is presented for the nonlinear pendulum covering the low, medium and high regimes of the pendulum motion. In addition, the behavior of the pendulum velocity, potential and kinetic energies is investigated in all regimes. Numerical integration in the form of Gaussian quadrature with 9 quadrature points proved sufficient in solving the elliptic integral of the first kind which represents the behavior of the nonlinear pendulum. Also, the power series solution is calculated here for all regimes and used as the exact solution for comparison purposes. A regression based equation for the period in the low and medium regimes is given in terms of the amplitude and length of the pendulum. The equation was successfully used to calculate the gravitational acceleration in terms of the measured values of the pendulum length, period and amplitude.

nonlinear pendulum, elliptic integrals, numerical integration, Gaussian quadrature, period, velocity, potential energy, kinetic energy, gravitational acceleration.