#### Consortium for Mathematics and its Applications

Product ID: 99577
Supplementary Print
High School

# Harmonic Motion and the Circular Functions (UMAP)

### Author: Dorothea D. Bone

A unit that involves precalculus, harmonic motion, and circular functions. In this module an explanation of simple harmonic motion is presented. The basic definitions are given with reference to a weight bobbing up and down on a spring. The formulas for instantaneous displacement is developed. The unit ends with a comparison of general sine and cosine functions, the formulas for displacement, and their graphs.

1. SIMPLE HARMONIC MOTION
1.1 Introduction
1.2 The Motion of a Shadow as an Example

2. A VIBRATING SPRING
2.1 Key Definitions
2.2 A Formula for Displacement
2.3 Sample Problem

3. A PENDULUM AS SIMPLE HARAMONIC MOTION
3.1 The Simple Pendulum

4. PHASE SHIFT
4.1 Out of Phase?
4.2 Sample Problem

5. EQUATIONS FROM GRAPHS
5.1 Review of Amplitude, Period, and Phase Shift
5.2 Some Examples
5.3 General Sine and Cosine Functions

6. SAMPLE EXAM UMAP Module
24 pages

#### Mathematics Topics:

• Precalculus & Trigonometry

#### Application Areas:

• Physical Sciences ,
• Harmonic Motion

#### Prerequisites:

Sine and cosine functions (graphs, radian measure, angular velocity); periodic function

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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