Nonlinear Systems & Linearization · Hard problem

A pendulum obeys $x' = y,\; y' = -16\sin x$ ($x$ the angle from the bottom, $y$ the angular velocity). It is released from rest at $x = \dfrac{\pi}{3}$. Using the conserved energy $E = \dfrac{y^2}{2} - 16\cos x$, find its angular speed $|y|$ as it swings through the bottom ($x=0$).