In an attempt to learn EJS, I started to do simple pendulum simulation since there are a lots of those already available over the internet. I am starting off with the differential equation, a = -(g/L) sin q where a is the angular acceleration and q is the angle of the string with respect to the vertical. My amplitude drops with time. Note that I have not introduced any damping. My plot of w vs. q are ellipse which spiral down towards the center with time (expected). I have googled to find solution to exact solution to this equation.

I saw one of your simple pendulums. I did not see its source. Are you assuming small angle oscillations?

Thanks