Computer Program Detail Page
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
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)
Building Functions (9-12)
Trigonometric Functions (9-12)
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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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: Properties of Periodic Motion
Is a Teaching Guide For Physics Classroom: Motion of a Mass on a Spring
Is a Teaching Guide For Physics Classroom: Vibrational Motion
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Is Supplemented By