 Vernier Software & Technology

# Physical Pendulum

## Introduction

The introductory treatment of the motion of a pendulum leaves one with the impression that the period of oscillation is independent of the mass and the amplitude, and depends only on the length of the pendulum. These relationships are generally true so long as two important conditions are met:

1. the amplitude is small (<< 1 radian), and
2. the mass of the system is concentrated at the end of the string.

Experiment 17 examined the non-ideal behavior of the pendulum when the amplitude was not kept small. In this experiment, you will investigate the effect on the behavior of a pendulum when the mass of the system can no longer be treated as a point mass at the end of a massless string.

## Objectives

In this experiment, you will

• Collect angle vs. time data for a variety of physical pendulums.
• Determine the period of oscillation from an analysis of the angle vs. time graph.
• From an analysis of the torques acting on the system, derive the equation describing the motion of the physical pendulum.
• Compare this equation to the one that describes the motion of a simple pendulum.
• Relate the angular frequency, ω, of the system to its physical features.
• Compare the agreement between experimental and calculated values of ω determined by this treatment of the system with those obtained by treating the system as if it were a simple pendulum.

## 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 18 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.