• 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.

• 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.

• 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.

• 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.

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

• F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

• 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 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.

• Physical Sciences K-8 Simple Harmonic Motion Unit
• Physics First Simple Harmonic Motion Unit
• Conceptual Physics Simple Harmonic Motion Unit
• Algebra-Based Physics Simple Harmonic Motion Unit
• AP/Calculus-Based Physics Simple Harmonic Motion Unit