# 22. Torque and the Simple Harmonic Oscillator

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## Learning Objectives

• Be able to calculate moments of inertia for compound objects.
• Be able to use the torque law to derive differential equations for a systems undergoing periodic or simple harmonic motion such as a simple pendulum, physical pendulums or torsional spring oscillators.
• Know how to apply the small angle approximation in order to get the simple harmonic oscillator equation for a simple pendulum and physical pendulums, and determine the period (or angular frequency) of the motion.

## Preparation

### Course Notes

Chapter 13.6. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: with Modern Physics. 12th ed. San Francisco, CA: Addison-Wesley, 2007. ISBN: 9780805321876.

## Lecture Video

### Video Excerpts

Watch the following excerpts from the Physics I lecture videos:

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## Learning Activities

### Guided Activities

Read through the class slides carefully. They explain all of the concepts from the module.

Slides: Torque and the Simple Harmonic Oscillator (PDF - 1.6MB)

### Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems. If you are struggling with the Challenge Problems, watch the Homework Help Session videos, which will give you tips on how to tackle problems of this type.

### Concept Questions

Concept Questions (PDF)

Solutions (PDF)

### Challenge Problems

Challenge Problems (PDF)

Solutions (PDF - 1.4MB)

## Problem Solving Help

In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.

### Help Session 1

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» iTunes U (MP4 - 25MB)
» Internet Archive (MP4 - 25MB)

### Help Session 2

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» iTunes U (MP4 - 56MB)
» Internet Archive (MP4 - 56MB)

### Help Session 3

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» iTunes U (MP4 - 9MB)
» Internet Archive (MP4 - 9MB)

## Related Resources

There are countless resources available online to help you learn physics. Try these:

• Read the Physics material on Connexions:
• Read through the materials on HyperPhysics:
• Try out the Pendulum Lab interactive simulation from PhET.

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