EJSS pendulum model

EJSS SHM pendulum model with t vs $ \theta $ graph
EJSS simple harmonic motion pendulum model with t vs $ \theta $ graph
based on models and ideas by

http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html
EJSS SHM pendulum model with t vs $ \theta $ graph
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvapendulumv2/SHMxvapendulumv2_Simulation.html
source code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvapendulumv2.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

1. lookang http://weelookang.blogspot.sg/2014/02/ejss-shm-model-with-vs-x-and-v-vs-x.html
2. lookang http://weelookang.blogspot.sg/2010/06/ejs-open-source-simple-harmonic-motion.html?q=SHM
3. lookang http://weelookang.blogspot.sg/2013/02/ejs-open-source-vertical-spring-mass.html?q=vertical+spring
4. lookang http://weelookang.blogspot.sg/2010/06/physical-quantities-and-units.html?q=pendulum
5. Wolfgang Christian and Francisco Esquembre http://www.opensourcephysics.org/items/detail.cfm?ID=13103

http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html
EJSS SHM pendulum model with t vs $ \theta $ graph
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvapendulumv2/SHMxvapendulumv2_Simulation.html
source code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvapendulumv2.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

commons terms associated with pendulum http://en.wikipedia.org/wiki/File:Simple_gravity_pendulum.svg#file

Assumption of this simple pendulum model:

1. The rod or cord on which the bob swings is massless, inextensible and always remains taut;
2. The bob is a point mass;
3. Motion occurs only in two dimensions, i.e. the bob does not trace an ellipse but an arc.
4. The motion does not lose energy to friction or air resistance.

Assumptions of SHM comparable to pendulum:

1. Motion approximates SHM when the angle $ \theta$ of oscillation is small, where $ sin \theta \approx \theta $

The equations that model the motion of the pendulum system are:

this model assumes

$ \frac{\delta \theta}{\delta t} = \omega $

$ \frac{\delta \omega}{\delta t} = -\frac{g}{L}( sin \theta)  $

where the terms

$ L $ represents the fixed length of the pendulum 

$  g $ represents the gravity force component as a result of Earth's pull.

If the motion starts to the positive amplitude position:

$ \theta = 5 degree $

$ \theta = 10 degree $

$ \theta = 15 degree $

$ \theta = 20 degree $

$ \theta = 25 degree $

$ \theta = 30 degree $

$ \theta = 40 degree $

$ \theta = 50 degree $

$ \theta = 60 degree $

$ \theta = 70 degree $

$ \theta = 80 degree $

$ \theta = 90 degree $

General Rule of Thumb

Thus, in general, the pendulum's swing motion is approximately a simple harmonic motion only when the Motion's angle $ \theta$ of oscillation is small, where $ sin \theta \approx \theta $, rule of thumb is about 5 degree!