Using either Lagrangian or Newtonian mechanics it's possible to obtain the equation of motion as the 2nd order nonlinear differential equation \[ \ddot{ \theta } = {-g \over l} \sin{\theta} .\] However there is no analytic solution to this equation but if the small angle approximation is applied ( \( \sin{\theta} \approx \theta \) ) then the equation of motion becomes, \[ \ddot{ \theta } = {-g \over l} \theta ,\] which has a solution of the form \[ \theta = \theta_0 \cos{(\sqrt{ {g \over l} } t}) .\] If you want to not use the small angle approximation then the ODE can be evaluated numerically using the fourth order Runge-Kutta method by first converting the 2nd order ODE into the two 1st order ODE's by letting \( u = \theta \) and \( v = \dot{\theta} \) we have \[ \dot{u} = v \] \[ \dot{v} = \frac{-g}{l} \sin{u} .\] Below is a simulation of the behavior of the two solutions:

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