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written by Andrew Duffy
This computer model shows the the connection between uniform circular motion and simple harmonic motion by animating the movement of two spring/mass systems. Users can set amplitude, mass, and spring constant so the blocks have different angular frequencies. As the block/spring system moves, watch what happens to the corresponding circular motion animation. This connection is one way to justify the basic equation of motion for an object experiencing simple harmonic motion.  This equation also corresponds to one dimension of uniform circular motion.  In this simulation, the author goes beyond the equation to explore the phase angle. There are analogous equations for the velocity and the acceleration as a function of time.

The Connection between Circular and Simple Harmonic Motion model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_bu_reference_circle.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java (JRE).
View the source code document attached to this resource
Subjects Levels Resource Types
Classical Mechanics
- Motion in Two Dimensions
= 2D Velocity
Oscillations & Waves
- Oscillations
= Simple Harmonic Motion
= Springs and Oscillators
- Lower Undergraduate
- High School
- Upper Undergraduate
- Instructional Material
= Activity
= Interactive Simulation
- Audio/Visual
= Movie/Animation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
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Mirror:
http://physics.bu.edu/~duffy/Ejs/…
Access Rights:
Free access
License:
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Andrew Duffy, Boston University
Keywords:
SHM, amplitude, circular, connection, harmonic, simple, spring motion
Record Cloner:
Metadata instance created May 2, 2010 by Mario Belloni
Record Updated:
May 24, 2013 by Matt Mohorn
Last Update
when Cataloged:
April 16, 2010
Other Collections:

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

High School — Functions (9-12)

Interpreting Functions (9-12)
  • F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?
Building Functions (9-12)
  • F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.?
Trigonometric Functions (9-12)
  • F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?
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Record Link
AIP Format
A. Duffy, Computer Program BOSTON UNIVERSITY PHYSICS: CONNECTION BETWEEN CIRCULAR AND SIMPLE HARMONIC MOTION MODEL (2010), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651).
AJP/PRST-PER
A. Duffy, Computer Program BOSTON UNIVERSITY PHYSICS: CONNECTION BETWEEN CIRCULAR AND SIMPLE HARMONIC MOTION MODEL (2010), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651>.
APA Format
Duffy, A. (2010). Boston University Physics: Connection between Circular and Simple Harmonic Motion Model [Computer software]. Retrieved April 19, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651
Chicago Format
Duffy, Andrew. "Boston University Physics: Connection between Circular and Simple Harmonic Motion Model." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651 (accessed 19 April 2014).
MLA Format
Duffy, Andrew. Boston University Physics: Connection between Circular and Simple Harmonic Motion Model. Computer software. 2010. Java (JRE) 1.5. 19 Apr. 2014 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651>.
BibTeX Export Format
@misc{ Author = "Andrew Duffy", Title = {Boston University Physics: Connection between Circular and Simple Harmonic Motion Model}, Month = {April}, Year = {2010} }
Refer Export Format

%A Andrew Duffy
%T Boston University Physics: Connection between Circular and Simple Harmonic Motion Model
%D April 16, 2010
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651
%O application/java

EndNote Export Format

%0 Computer Program
%A Duffy, Andrew
%D April 16, 2010
%T Boston University Physics: Connection between Circular and Simple Harmonic Motion Model
%8 April 16, 2010
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651


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Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The AJP/PRST-PER presented is based on the AIP Style with the addition of journal article titles and conference proceeding article titles.

The APA Style presented is based on information from APA Style.org: Electronic References.

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Boston University Physics: Connection between Circular and Simple Harmonic Motion Model:

Is Supplemented By Boston University: Simple Harmonic Motion Lecture Notes

Background information on SHM and uniform circular motion, also by the author of the Connection Between Circular and Simple Harmonic Motion computer model.

relation by Caroline Hall
Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Connection between Circular and Simple Harmonic Motion.

relation by Mario Belloni
Is a Teaching Guide For Physics Classroom: Vibrational Motion

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