 Vernier Software & Technology

# Simple Harmonic Motion: Mathematical Model

## Introduction

When you suspend an object from a spring, the spring will stretch. If you pull on the object and release it, it will begin to oscillate up and down. In this experiment, you will examine this kind of motion, perform a curve fit on the position-time graph, and relate the parameters of the equation with physical features of the system.

## Objectives

In this experiment, you will

• Collect position vs. time data as a mass, hanging from a spring, is set in an oscillating motion.
• Determine the best fit equation for the position vs. time graph of an object undergoing simple harmonic motion (SHM).
• Define the terms amplitude, offset, phase shift, period and angular frequency in the context of SHM.
• Relate the parameters in the best-fit equation for a position vs. time graph to their physical counterparts in the system.
• Use deductive reasoning to predict the system mass required to produce a given value of angular frequency in the curve fit to SHM.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?

## Advanced Physics with Vernier — Mechanics

See other experiments from the lab book.

 1 Motion on an Incline 2 Error Analysis 3 Newton's First Law 4 Newton's Second Law 5 Newton's Third Law 6 Projectile Motion 7 Energy Storage and Transfer: Elastic Energy 8 Energy Storage and Transfer: Kinetic Energy 9 Energy Storage and Transfer: Gravitational Energy 10A Impulse and Momentum (Motion Detector) 10B Impulse and Momentum (Photogate) 11A Momentum and Collisions (Motion Detectors) 11B Momentum and Collisions (Photogates) 12A Centripetal Acceleration 12B Centripetal Acceleration 13 Rotational Dynamics 14 Conservation of Angular Momentum 15 Simple Harmonic Motion: Mathematical Model 16 Simple Harmonic Motion: Kinematics and Dynamics 17 Pendulum Periods 18 Physical Pendulum 19 Center of Mass

### Experiment 15 from Advanced Physics with Vernier — Mechanics Lab Book #### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.