# 15. Mechanical Energy and the Simple Harmonic Oscillator

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## Learning Objectives

• Learn that a mass-spring system has a quadratic potential energy.
• Explain how conservation of energy leads to periodic motion for a mass-spring system.
• Be able to qualitatively describe the motion of a mass-spring system. Understand what it means for the motion to be of periodic (in time) and harmonic (in space).
• Be able to identify the force restoring on a system undergoing simple harmonic motion.
• Be able to find the differential equation describing the motion of system undergoing simple harmonic motion using energy techniques or force techniques.
• Explain the meaning of frequency and be able to experimentally determine frequency of a mass-spring oscillator.
• Explain the difference between the concepts of angular frequency and angular velocity.
• Be able find the angular frequency and period for a system undergoing simple harmonic motion.
• Explain the mathematical function that describes simple harmonic motion.
• Be able to use given information in a problem to describes the constants that appear in the the mathematical function that describes simple harmonic motion.
• Be able to appropriate the equations of motion for a system for small oscillations.

## Preparation

### Course Notes

Chapter 13.1-13.5. 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.

### 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 - 3.2MB)

## Problem Solving Help

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

### Help Session 1

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/mechanical-energy-and-the-simple-harmonic-oscillator/help-session-1/uPWOTSLxuwQ.srt'}

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### Help Session 2

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### Help Session 3

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### Help Session 4

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### Help Session 5

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### Help Session 6

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### Help Session 7

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### Help Session 8

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### Help Session 9

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## Related Resources

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