NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
February 20, 2020, 04:05:11 am

Wisdom is to teach our students how to teach themselves. ...Wisdom

 Pages: [1]   Go Down
 Author Topic: EJSS Circular Motion to Simple Harmonic Motion Model  (Read 2201 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
lookang
Moderator
Hero Member

Offline

Posts: 1793

http://weelookang.blogspot.com

 « 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
 image8.png (47.94 KB, 700x586 - viewed 451 times.) *** There are 2 more attached files. You need to login to acces it! « Last Edit: February 15, 2015, 01:16:23 pm by lookang » Logged
 Pages: [1]   Go Up
Wisdom is to teach our students how to teach themselves. ...Wisdom