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 Author Topic: EJSS Circular Motion to Simple Harmonic Motion Model  (Read 1714 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
lookang
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 « Embed this message on: February 15, 2015, 01:13:33 pm » posted from:New York,New York,United States

EJSS Circular Motion to Simple Harmonic Motion Model

Example 3: Uniform Circular motion’s one dimensional projection

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 x−y plane, then its motion along each coordinate is simple harmonic motion with amplitude A and angular frequency ω.

https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcircle/SHMcircle_Simulation.html

Q1: given that, a circular motion can be described by x = A cos(ω t) and y A sin(ω t) what is the y-component model-equation that can describe the motion of a uniform circular motion?

A1: y = Asin (ωt)
Q2: When the x-component of the circular motion is modelled by x = A cos(ω t) and y A sin(ω t) suggest an model-equation for y.

A2: y = Acos (ωt) for top position or y = - Acos (ωt) for bottom position
Q3: explain why are the models for both x and y projection of a uniform circular motion, a simple harmonic motion?

A3: both x = A cos(ω t) and y A sin(ω t) each follow the defining relationship for SHM as ordinary differential equations of d 2 x d t 2 = - ω 2 x and d 2 y d t 2 = - ω 2 y respectively.
Run Model:

https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcircle/SHMcircle_Simulation.html
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"That their main business was not put into the mind knowledge which was not there before, but to turn the mind's eye towards light so that it might see for itself." ...Plato's advice to educators(429-347BC)