practice of mathematical modeling added
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| simple play and observe http://weelookang.blogspot.sg/2015/01/shm-chapter-03.html Run: Link1, Link2 Download and Unzip: Link1, Link2 Source File: Link1, Link2
author: lookang
author of EJSS 5.0 Francisco Esquembre
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| 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 field http://weelookang.blogspot.sg/2015/01/shm-chapter-03.html Run: Link1, Link2 Download and Unzip: Link1, Link2 Source File: Link1, Link2
author: lookang
author of EJSS 5.0 Francisco Esquembre
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| 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.html Run: Link1, Link2 Download and Unzip: Link1, Link2 Source File: Link1, Link2
author: lookang
author of EJSS 5.0 Francisco Esquembre
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| 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.html Run: Link1, Link2 Download and Unzip: Link1, Link2 Source File: Link1, Link2
author: lookang
author of EJSS 5.0 Francisco Esquembre
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| 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 field http://weelookang.blogspot.sg/2015/01/shm-chapter-03.html Run: Link1, Link2 Download and Unzip: Link1, Link2 Source File: Link1, Link2
author: lookang
author of EJSS 5.0 Francisco Esquembre
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EJSS circle motion to SHM model
EJSS simple harmonic motion to circular motion model with phase difference
based on models and ideas by
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| 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 |
- lookang http://weelookang.blogspot.sg/2012/07/ejs-open-source-phase-difference-java.html
- lookang http://weelookang.blogspot.sg/2013/02/ejs-open-source-vertical-spring-mass.html?q=vertical+spring
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| 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:
$ \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} $ 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 $.
and
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) $
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