# 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.** Table of Contents: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**

7. ANSWERS TO EXERCISES

8. ANSWERS TO SAMPLE EXAM

7. ANSWERS TO EXERCISES

8. ANSWERS TO SAMPLE EXAM

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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