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written by Andrew Duffy
This interactive simulation offers a way for students to explore the connection between uniform circular motion and simple harmonic motion.  The display shows two blocks on springs oscillating horizontally, and two balls traveling in uniform motion in a circular path.  The user sets initial values for the blocks: amplitude, mass, and spring constant. The two balls are automatically set to the same values. Students are able to see that the circular motion of each ball corresponds to the motion of the blocks, thus promoting understanding of the basic equation for objects undergoing simple harmonic motion.

To extend the learning, users can set values for the phase angles of each block. Also included by the author is a set of suggested activities to accompany the simulation.


The Connection between Circular and Simple Harmonic Motion model was created using the Easy Java Simulations (EJS) modeling tool.

Please note that this resource requires at least version 1.5 of Java (JRE).
Editor's Note: A mass on a spring will trace out a sinusoidal pattern as a function of time, a characteristic of any object vibrating in simple harmonic motion. You can view this pattern by clicking "Show Motion Graphs" while the model is running. See Related Materials for supplementary lecture notes by the same author.
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
- High School
- Lower Undergraduate
- Upper Undergraduate
- Instructional Material
= Activity
= Interactive Simulation
- Audio/Visual
= Movie/Animation
Appropriate Courses Categories Ratings
- Conceptual Physics
- Algebra-based Physics
- AP Physics
- Activity
- New teachers
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Intended Users:
Learner
Educator
Format:
application/java
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:
June 2, 2014 by Andreu Glasmann
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.?

This resource is part of a Physics Front Topical Unit.


Topic: Kinematics: The Physics of Motion
Unit Title: Circular Motion

This interactive simulation offers a way for students to explore the connection between uniform circular motion and simple harmonic motion. It provides a way to visualize SHM as the projection of uniform circular motion onto one axis, which should promote understanding of the basic equation for objects undergoing simple harmonic motion.

Link to Unit:
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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 December 21, 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 21 December 2014).
MLA Format
Duffy, Andrew. Boston University Physics: Connection between Circular and Simple Harmonic Motion Model. Computer software. 2010. Java (JRE) 1.5. 21 Dec. 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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The AIP Style presented is based on information from the AIP Style Manual.

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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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