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

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.

Connection between Circular and Simple Harmonic Motion Source Code
The source code zip archive contains an XML representation of the Connection between Circular and Simple Harmonic Motion model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 6kb .zip
Published: April 27, 2010
previous versions

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.

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=10014">Duffy, Andrew. "Boston University Physics: Connection between Circular and Simple Harmonic Motion Model."</a>

A. Duffy, Computer Program BOSTON UNIVERSITY PHYSICS: CONNECTION BETWEEN CIRCULAR AND SIMPLE HARMONIC MOTION MODEL (2010), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651).

A. Duffy, Computer Program BOSTON UNIVERSITY PHYSICS: CONNECTION BETWEEN CIRCULAR AND SIMPLE HARMONIC MOTION MODEL (2010), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651>.

Duffy, A. (2010). Boston University Physics: Connection between Circular and Simple Harmonic Motion Model [Computer software]. Retrieved September 25, 2023, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651

Duffy, Andrew. "Boston University Physics: Connection between Circular and Simple Harmonic Motion Model." https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651 (accessed 25 September 2023).

@misc{
Author = "Andrew Duffy",
Title = {Boston University Physics: Connection between Circular and Simple Harmonic Motion Model},
Month = {April},
Year = {2010}
}

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

%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 https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651

Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

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

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.