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Spring Motion Model

written by
Andrew Duffy

The Spring Motion Model shows the motion of a block attached to an ideal spring. The block can oscillate back-and-forth horizontally. Users can change the mass of the block, the spring constant of the spring, and the initial position of the block. You can then see the resulting motion of the block, as well as see bar graphs of the energy and plots of the block's position, speed, and acceleration as a function of time.

The Spring 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).

Editor's Note:Students often struggle to recognize the connection between the oscillation of a mass on a spring and the sinusoidal nature of simple harmonic motion. See Related Materials for an interactive homework problem that takes learners step-by-step through each component of a "block and spring" exercise. It provides free-body diagrams, conceptual analysis, and explicit support in using the Work-Kinetic Energy Theorem to solve the problem.

Spring Motion Model Source Code
The source code zip archive contains an XML representation of the Spring 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

6-8: 4E/M1. Whenever energy appears in one place, it must have disappeared from another. Whenever energy is lost from somewhere, it must have gone somewhere else. Sometimes when energy appears to be lost, it actually has been transferred to a system that is so large that the effect of the transferred energy is imperceptible.

6-8: 4E/M2. Energy can be transferred from one system to another (or from a system to its environment) in different ways: 1) thermally, when a warmer object is in contact with a cooler one; 2) mechanically, when two objects push or pull on each other over a distance; 3) electrically, when an electrical source such as a battery or generator is connected in a complete circuit to an electrical device; or 4) by electromagnetic waves.

9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.

4F. Motion

9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.

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/M4. Simulations are often useful in modeling events and processes.

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.^{?}

Trigonometric Functions (9-12)

F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^{?}

This resource is part of a Physics Front Topical Unit.

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

This Java model explores the motion of a block attached horizontally to an ideal spring. You can change the mass of the block, spring constant, and initial position. The model will display energy bar graphs and graphs of position, speed, and acceleration as a function of time. Try teaming this simulation with the interactive homework problem (directly below) to promote deep understanding of the sinusoidal nature of SHM.

Duffy, A. (2010). Spring Motion Model [Computer software]. Retrieved January 24, 2022, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10015&DocID=1653

%A Andrew Duffy %T Spring Motion Model %D April 16, 2010 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10015&DocID=1653 %O application/java

%0 Computer Program %A Duffy, Andrew %D April 16, 2010 %T Spring Motion Model %8 April 16, 2010 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=10015&DocID=1653

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Interactive homework problem provides step-by-step help in solving a problem that involves a block attached to a spring. Includes conceptual analysis and support in using the Work-Kinetic Energy Theorem.