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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.
Last Modified May 24, 2013
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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.
Published April 27, 2010
Last Modified May 2, 2010