This interactive simulation models the motion of a simple pendulum. How is the motion of the pendulum affected by changing length of the string, initial angle, and mass of the bob? Adjust the acceleration due to gravity to simulate pendulum motion on another planet. Energy bar graphs can be displayed in stepped motion alongside the swinging pendulum to get a clear picture of kinetic/potential energy conversion. Click on "Forces" to see free body diagrams. Advanced learners can view graphs of angular position, angular velocity, and angular acceleration as well.

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:This model is simple enough for middle school students to manipulate, yet provides an array of robust tools that also render it appropriate for high school or AP physics courses. See Related Materials for a multi-day module on simple harmonic motion (Science NetLinks) and for instructions on installing and running the cost-free EJS Modeling and Authoring Tool.

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.

9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.

4F. Motion

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

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

3-5: 11B/E3. A model of something is similar to, but not exactly like, the thing being modeled. Some models are physically similar to what they are representing, but others are not.

6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Functions (8)

Use functions to model relationships between quantities. (8)

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

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.^{?}

This resource is part of a Physics Front Topical Unit.

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

This robust, yet easy-to-use interactive model can be adapted for learners ranging from middle school through AP physics. You can change the string length, mass, and initial angle. Change the gravitational constant to see how the pendulum moves on different planets. View real-time bar graphs to see how energy is converted from kinetic-to-potential and back as the pendulum swings. Advanced learners can view graphs of angular acceleration/velocity.

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=9409">Duffy, Andrew. Boston University Physics Easy Java Simulation: Simple Pendulum. August 27, 2009.</a>

Duffy, A. (2009, August 27). Boston University Physics Easy Java Simulation: Simple Pendulum. Retrieved September 24, 2023, from http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html

Duffy, Andrew. Boston University Physics Easy Java Simulation: Simple Pendulum. August 27, 2009. http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html (accessed 24 September 2023).

%A Andrew Duffy %T Boston University Physics Easy Java Simulation: Simple Pendulum %D August 27, 2009 %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html %O application/java

%0 Electronic Source %A Duffy, Andrew %D August 27, 2009 %T Boston University Physics Easy Java Simulation: Simple Pendulum %V 2023 %N 24 September 2023 %8 August 27, 2009 %9 application/java %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html

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A link to the Easy Java Simulations Modeling and Authoring tool, needed to explore the computational model used in the simple pendulum model (cost free)

A standards-based module on the pendulum for grades 7-9 that includes lesson plan, student activity sheets, assessment, related simulations, and background information.

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.