## Monday, February 24, 2014

### EJSS circle motion to SHM model

Update 10 July 2015

## practice of mathematical modeling added

 select a model (TEAL) that can describe simulated data (BLUE), note that Y = 2*sin(t) is too big compared to ϑ1 BLUE's motion, which you can select from drop-down menu and modify through input fieldhttp://weelookang.blogspot.sg/2015/01/shm-chapter-03.htmlRun: Link1, Link2Download and Unzip: Link1, Link2Source File: Link1, Link2 author: lookang author of EJSS 5.0 Francisco Esquembre

 select a model (TEAL) that can describe simulated data (BLUE), note that Y = 0.97*sin(t) fits well  to ϑ1 BLUE's motion, http://weelookang.blogspot.sg/2015/01/shm-chapter-03.htmlRun: Link1, Link2Download and Unzip: Link1, Link2Source File: Link1, Link2 author: lookang author of EJSS 5.0 Francisco Esquembre

 Play and observe that the model (TEAL) can describe simulated data (BLUE), note that Y = 0.97*sin(t) for another period of extended play.http://weelookang.blogspot.sg/2015/01/shm-chapter-03.htmlRun: Link1, Link2Download and Unzip: Link1, Link2Source File: Link1, Link2 author: lookang author of EJSS 5.0 Francisco Esquembre

 select a model (TEAL) that can describe simulated data (MAGENTA), note that Y = -0.88*cos(t) fits well to to ϑ2 (MAGENTA)'s motion, which you can select from drop-down menu and modify through input fieldhttp://weelookang.blogspot.sg/2015/01/shm-chapter-03.htmlRun: Link1, Link2Download and Unzip: Link1, Link2Source File: Link1, Link2 author: lookang author of EJSS 5.0 Francisco Esquembre

EJSS circle motion to SHM model
EJSS simple harmonic motion to circular motion model with phase difference
based on models and ideas by
 http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html EJSS circle motion to SHM model https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcircle/SHMcircle_Simulation.html source code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcircle.zip experimental http://phonegap.com/ android app: https://dl.dropboxusercontent.com/u/44365627/EJSScirclemotiontoSHMmodel-debug%20%281%29.apk author: lookang author of EJSS 5.0 Francisco Esquembre

 http://weelookang.blogspot.sg/2014/02/ejss-pendulum-model.html EJSS circle motion to SHM model https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcircle/SHMcircle_Simulation.html source code: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcircle.zip experimental http://phonegap.com/ android app: https://dl.dropboxusercontent.com/u/44365627/EJSScirclemotiontoSHMmodel-debug%20%281%29.apk author: lookang author of EJSS 5.0 Francisco Esquembre

## Description:

In physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. The distance of the body from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, is responsible for a centripetal force which is also constant in magnitude and directed towards the axis of rotation.

## The equations that model the motion of the circular motion are:

this uniform $\omega_{1}$ =$\omega_{2}$ circular motion model assumes

$\frac{\delta \theta_{1}}{\delta t} = \omega_{1}$

$\frac{\delta \theta_{2}}{\delta t} = \omega_{2}$

where the terms

$\theta_{1}$ and $\theta_{2}$ represents the angle of rotation in uniform circular motion

$\omega_{1}$ and $\omega_{2}$ are constants equal to each other.
in circular motion,

$\theta_{1} = \omega_{1} t$

$\theta_{2} = \omega_{2} t$

results in phase difference of

$\phi = \theta_{1} - \theta_{2}$ when rotation is clockwise

$\phi = \theta_{2} - \theta_{1}$ when rotation is anti-clockwise viewed from your perspective.

Simple harmonic motion can in some cases be considered to be the one-dimensional projection of uniform circular motion. If an object moves with angular speed $\omega$ around a circle of radius $A$ centered at the origin of the $x-y$ plane, then its motion along each coordinate is simple harmonic motion with amplitude $A$ and angular frequency $\omega$.

## The simplified equations that model the motion projection of circular motion = simple harmonic motion are:

if $y_{1} = A_{1} cos (\omega_{1}t )$

then $y_{2} = A_{2} cos (\omega_{2}t - \phi)$

and

if $x_{1} = -A_{1} sin(\omega_{1}t )$

then $x_{2} = A_{2} sin (\omega_{2}t + \phi)$