# Differential equation for the simple pendulum

Celso
Homework Statement:
A simple pendulum whose length is ##l = 9.8m## satisfies the equation ##\dddot\theta + sin(\theta) = 0##
If ##\Theta_{0}## is the amplitude of oscillation, show that its period ##T## is given by
##T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{(1-\alpha sin(\phi)^2)^{1/2}}## where ##\alpha = sin(\frac{1}{2}\Theta)^2##
Relevant Equations:
##T = \frac{2\pi}{\omega}##
How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0##
How is this right if the ##\theta## time dependence is not given?