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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"

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 Author Topic: Pendulum sets with different initial angle plus damping  (Read 4723 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
ahmedelshfie
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 « Embed this message on: December 06, 2010, 04:39:26 pm » posted from:SAO PAULO,SAO PAULO,BRAZIL

This applet Created by prof Hwang, modified by Ahmed.
Original applet Pendulum sets with different initial angle plus damping
This simulation show 11 pendulums with different initial angle(from minimum angle to minimum angle+angle range)
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 factor are the same for all pendulums. Do you know why?

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