Subject: Pendulum-potential, kinetic energy vs time

My physics teacher asked us to draw a graph of the gravitational potential 
energy (GPE) and the kinetic energy (KE) of a swinging pendulum versus time, 
for one swing of the pendulum.

His graph was parabola-shaped, with the GPE starting off at the top, hitting 
its minimum at the midway point, and returning to the top at the end of the 
swing. The KE graph was identical to the GPE graph but upside-down.

However, this could not be true, because the pendulum must slow down before it 
changes direction (the teacher's original answer would produce a non-
differentiable function when continued over more than one swing). I brought 
this to my teacher's attention and he recognized that the parabola graph was 
wrong. However, even after going through all his calculus books, he could not 
find a way to construct the correct graph. I know it looks *something* like a 
sine wave...

My question is, how would one find the correct graph of this? (I have taken AP 
Calculus so descriptions using derivatives, etc. are fine)

Re: Pendulum-potential, kinetic energy vs time