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#### Description:

This interactive simulation offers a way for students to explore the connection between uniform circular motion and simple harmonic motion. The display shows two blocks on springs oscillating horizontally, and two balls traveling in uniform motion in a circular path. The user sets initial values for the blocks: amplitude, mass, and spring constant. The two balls are automatically set to the same values. Students are able to see that the circular motion of each ball corresponds to the motion of the blocks, thus promoting understanding of the basic equation for objects undergoing simple harmonic motion. To extend the learning, users can set values for the phase angles of each block. Also included by the author is a set of suggested activities to accompany the simulation. See Related Materials for an extensive online multimedia tutorial from PhysClips on the topic of simple harmonic motion. 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.

#### Subjects:

• Education > General
• Mathematics > General

English

#### Access Privileges:

Public - Available to anyone

Creative Commons Attribution Non-Commercial Share Alike

#### Collections:

None
Update Standards?

#### CCSS.Math.Practice.MP4: Common Core State Standards for Mathematics

Model with mathematics.

#### CCSS.Math.Content.HSF-IF.B: Common Core State Standards for Mathematics

Interpret functions that arise in applications in terms of the context

#### CCSS.Math.Content.HSF-IF.B.4: Common Core State Standards for Mathematics

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.?

#### CCSS.Math.Content.HSF-IF.B.5: Common Core State Standards for Mathematics

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?

#### CCSS.Math.Content.HSF-IF.C: Common Core State Standards for Mathematics

Analyze functions using different representations

#### CCSS.Math.Content.HSF-IF.C.7: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSF-IF.C.7e: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSF-TF.A: Common Core State Standards for Mathematics

Extend the domain of trigonometric functions using the unit circle

#### CCSS.Math.Content.HSF-TF.A.1: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSF-TF.A.4: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSF-TF.B: Common Core State Standards for Mathematics

Model periodic phenomena with trigonometric functions

#### CCSS.Math.Content.HSF-TF.B.5: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-C.A: Common Core State Standards for Mathematics

Understand and apply theorems about circles

#### CCSS.Math.Content.HSG-C.A.4: Common Core State Standards for Mathematics

(+) Construct a tangent line from a point outside a given circle to the circle.
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