Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Differential Equations

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™ CAS

3.2

## Simple Harmonic Motion

#### Activity Overview

With an example of the motion of a child on a swing, the activity begins with the trigonometric function between time and displacement and differentiates up to acceleration.

#### Key Steps

• In Problem 1, students build an understanding of the concept of acceleration. They form the basis for deriving the forms for simple harmonic motion.

• They use key animations to understand simple harmonic motion. The animations will assist students in answering questions asked throughout the activity.

• Students establish that this forms the basis for deriving the forms for simple harmonic motion, beginning with the standard relationship between time and displacement, leading to velocity, and finally to acceleration.

Substituting back leads readily to the defining equation in terms of acceleration and displacement.