Introduction to Mechanics
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
Notes: Simple Harmonic Oscillation and Torque (PDF - 2.0MB)#
Suggested Textbook Reading (Optional)
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:
Download the complete lectures from this course:
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
Challenge Problems
Problem Solving Help
In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.
Help Session 1
Download this video:
» iTunes U (MP4 - 25MB)
» Internet Archive (MP4 - 25MB)
Help Session 2
Download this video:
» iTunes U (MP4 - 56MB)
» Internet Archive (MP4 - 56MB)
Help Session 3
Download this video:
» 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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