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## 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.

This applet was created with EJS, Easy Java Simulations, a modeling tool that allows users without formal programming experience to generate computer models and simulations.
Editor's Note: See Related Materials for an extensive online multimedia tutorial from PhysClips on the topic of simple harmonic motion.
Subjects Levels Resource Types
Oscillations & Waves
- Oscillations
= Simple Harmonic Motion
- High School
- Lower Undergraduate
- Middle School
- Upper Undergraduate
- Instructional Material
= Interactive Simulation
- Audio/Visual
= Movie/Animation
Appropriate Courses Categories Ratings
- Physical Science
- Physics First
- Conceptual Physics
- Algebra-based Physics
- AP Physics
- Laboratory
- New teachers
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Intended Users:
Learner
Educator
Format:
application/java
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:
acceleration, amplitude, centripetal acceleration, circular, function, harmonic, motion, phase, simple, simple harmonic motion, simulation, uniform circular motion
Record Cloner:
Metadata instance created September 2, 2009 by Elijah Lee
Record Updated:
November 12, 2012 by Caroline Hall
Last Update
when Cataloged:
August 27, 2009
Other Collections:

### AAAS Benchmark Alignments (2008 Version)

#### 2. The Nature of Mathematics

2A. Patterns and Relationships
• 9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.
2B. Mathematics, Science, and Technology
• 9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.

#### 4. The Physical Setting

4F. Motion
• 6-8: 4F/M7. Wave behavior can be described in terms of how fast the disturbance spreads, and in terms of the distance between successive peaks of the disturbance (the wavelength).
• 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.
• 9-12: 4F/H6c. The energy of waves (like any form of energy) can be changed into other forms of energy.
• 9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

#### 11. Common Themes

11B. Models
• 6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.
• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

### 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.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?
• F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?
• F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Trigonometric Functions (9-12)
• F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
• F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
• F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?

#### High School — Geometry (9-12)

Circles (9-12)
• G-C.4 (+) Construct a tangent line from a point outside a given circle to the circle.

This resource is part of a Physics Front Topical Unit.

Topic: Periodic and Simple Harmonic Motion
Unit Title: Simple Harmonic Motion

This simple, yet creative Java simulation offers a way for students to explore the connection between uniform circular motion and SHM.  It will help build understanding of the basic equation for objects undergoing simple harmonic motion. The editors suggest using this resource with the interactive homework problem "Block and Spring" directly below.

Link to Unit:
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Record Link
AIP Format
A. Duffy, (2008), WWW Document, (http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html).
AJP/PRST-PER
A. Duffy, Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion (2008), <http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html>.
APA Format
Duffy, A. (2009, August 27). Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion. Retrieved September 17, 2024, from http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html
Chicago Format
Duffy, Andrew. Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion. August 27, 2009. http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html (accessed 17 September 2024).
MLA Format
Duffy, Andrew. Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion. 2008. 27 Aug. 2009. 17 Sep. 2024 <http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html>.
BibTeX Export Format
@misc{ Author = "Andrew Duffy", Title = {Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion}, Volume = {2024}, Number = {17 September 2024}, Month = {August 27, 2009}, Year = {2008} }
Refer Export Format

%A Andrew Duffy %T Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion %D August 27, 2009 %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html %O application/java

EndNote Export Format

%0 Electronic Source %A Duffy, Andrew %D August 27, 2009 %T Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion %V 2024 %N 17 September 2024 %8 August 27, 2009 %9 application/java %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/reference_circle_v1.html

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### Boston University Physics Easy Java Simulation: Uniform Circular Motion and Simple Harmonic Motion:

Same topic as PhysClips: Simple Harmonic Motion

Multimedia tutorial provides extensive background support on simple harmonic motion through video, Flash animations, informative text, diagrams, and graphs.

relation by Caroline Hall
Is Part Of http://physics.bu.edu/~duffy/Ejs/

This is the full index of Easy Java Simulations (EJS) by author Andrew Duffy, created for first-semester introductory physics.  EJS is a modeling tool developed by the Open Source Physics project.

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

The Easy Java Simulations Modeling and Authopring Tool is needed to explore the computational model used in the Uniform Circular Motion and SHM model.

relation by Caroline Hall

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