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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).
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)
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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