[quote author=Fu-Kwun Hwang link=topic=2010.msg7572#msg7572 date=1291342118]
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)
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]

[quote author=Fu-Kwun Hwang link=topic=2010.msg7572#msg7572 date=1291342118]
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)
For the second mode: the period and damping factor are the same for all pendulums. Do you know why?

This is due to the small angle assumption say ? = 5 degree, the period T has to be the same for the all ? = 5 degree.

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).
is my interpretation of the question correct?