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

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).

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.^{?}

<a href="http://www.compadre.org/portal/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, (http://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), <http://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 January 23, 2017, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10014&DocID=1651

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 23 January 2017).

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

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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.

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