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])
1. $\frac{d^2\theta}{dt}=-\frac{\ell}{g}\sin\theta-b\frac{d\theta}{dt}$ (equation for real pendulum)
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this mode is demonstrate real pendulum swings at different period T for different magnitude of angle ?.
well done!
i like the view of all pendulum all superposition together.[img]http://www.phy.ntnu.edu.tw/ntnujava/index.php?action=dlattach;topic=2010.0;attach=3645;image[/img]

2. $\frac{d^2\theta}{dt}\approx-\frac{\ell}{g}\theta-b\frac{d\theta}{dt}$ (equation for small angle approximation :assume $\sin\theta\approx\theta$)
i don't understand the question on "damping factor are the same for all pendulums", if b = 0.5, it will be the same of all models of the pendulums because that is the way the model is made to obey this mathematical equation $\frac{d^2\theta}{dt}\approx-\frac{\ell}{g}\theta-b\frac{d\theta}{dt}$ (equation for small angle approximation :assume $\sin\theta\approx\theta$).