This simulation show 11 pendulums with different initial angle(from [u][i]minimum angle[/i][/u] to [u][i]minimum angle+angle range[/i][/u])
It can be run in two different modes:
1. $\frac{d^2\theta}{dt}=-\frac{\ell}{g}\sin\theta-b\frac{d\theta}{dt}$ (equation for real pendulum)
2. $\frac{d^2\theta}{dt}\approx-\frac{\ell}{g}\theta-b\frac{d\theta}{dt}$ (equation for small angle approximation :assume $\sin\theta\approx\theta$)

The damping factor b=0 is the default.
You can change it and find out what will happened.
For the second mode: the period and damping rate are the same for all pendulums. Do you know why?