## Tuesday, February 18, 2014

### 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.htmlEJSS SHM pendulum model with t vs $\theta$ graphhttps://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvapendulumv2/SHMxvapendulumv2_Simulation.htmlsource code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvapendulumv2.zipauthor: lookangauthor of EJSS 5.0 Francisco Esquembre

 http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.htmlEJSS SHM pendulum model with t vs $\theta$ graphhttps://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvapendulumv2/SHMxvapendulumv2_Simulation.htmlsource code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvapendulumv2.zipauthor: lookangauthor 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!