November 11, 2016

This interactive simulation models the motion of a simple pendulum. Users can explore how pendulum motion is 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. The model is simple enough for middle school students to manipulate, yet also provides an array of robust tools that render it appropriate for introductory 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. 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.

- Mathematics > General

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Model with mathematics.

Use functions to model relationships between quantities.

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.

Create equations that describe numbers or relationships

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

Analyze functions using different representations

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.?

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Extend the domain of trigonometric functions using the unit circle

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Model periodic phenomena with trigonometric functions

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?