# EJSS circle motion to SHM model

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 ω1 =ω2 circular motion model assumes

δθ1δt=ω1

δθ2δt=ω2

where the terms

θ1 and θ2 represents the angle of rotation in uniform circular motion

ω1 and ω2 are constants equal to each other.
in circular motion,

θ1=ω1t

θ2=ω2t

results in phase difference of

ϕ=θ1θ2 when rotation is clockwise

ϕ=θ2θ1 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 ω around a circle of radius A centered at the origin of the xy plane, then its motion along each coordinate is simple harmonic motion with amplitude A and angular frequency ω.

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

if y1=A1cos(ω1t)

then y2=A2cos(ω2tϕ)

and

if x1=A1sin(ω1t)

then x2=A2sin(ω2t+ϕ)

Posted by