[quote author=Fu-Kwun Hwang link=topic=2010.msg7633#msg7633 date=1292557129]
Why the angle \theta has to be smaller than 5 degree to be able to satisfy the small angle approximation?
Why 5.5 can not be a small angle? Does 5 a magic number???
[/quote]

students can key in 5/180*PI = 0.08726
in radian mode, students can key in sin(5/180*PI) = 0.08715
the students can realise the approximation is accurate for 2 decimal place only.

students can key in 5.5/180*PI = 0.09599
in radian mode, students can key in sin(5.5/180*PI) = 0.09584
the students can realize the approximation is accurate for 2 decimal place only.

it is a balance between practically observably angle of oscillation and accuracy in approximation of the assumption of  \frac{d^2\theta}{dt}\approx-\frac{\ell}{g}\theta-b\frac{d\theta}{dt}

[quote author=Fu-Kwun Hwang link=topic=2010.msg7633#msg7633 date=1292557129]
i don't understand the question on "damping factor are the same for all pendulums"
[/quote]
What I mean is "The period and damping rate are the same for all pendulums."

ic damping rate.
then my earlier answer is acceptable? made to obey this mathematical equation?