# EJSS pendulum model

EJSS SHM pendulum model with t vs θ graph
EJSS simple harmonic motion pendulum model with t vs θ graph
based on models and ideas by
 http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html EJSS SHM pendulum model with t vs θ 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

 http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html EJSS SHM pendulum model with t vs θ 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 θ of oscillation is small, where sinθθ

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

this model assumes

δθδt=ω

δωδt=gL(sinθ)

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:

 θ=5degree
 θ=10degree
 θ=15degree
 θ=20degree
 θ=25degree
 θ=30degree
 θ=40degree
 θ=50degree
 θ=60degree
 θ=70degree
 θ=80degree
 θ=90degree

## General Rule of Thumb

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

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