15. Mechanical Energy and the Simple Harmonic Oscillator

• Course Home
• Syllabus
• Introduction to Mechanics

  • 1. Units and Dimensional Analysis
  • 2. Problem Solving and Estimation
• Mathematics: The Language of Science

  • 3. Cartesian Coordinates and Vectors
• Translational Kinematics

  • 4. One-Dimensional Kinematics and Free Fall
  • 5. One-Dimensional Kinematics: Non-Constant Acceleration
  • 6. Two-Dimensional Kinematics
• Force and Newton's Laws of Motion

  • 7. Concept of Force
  • 8. Applications of Newton's Second Law
• Circular Motion

  • 9. Circular Motion Kinematics
  • 10. Circular Motion Dynamics
• Conservation of Energy

  • 11. Work and Energy
  • 12. Work and the Dot Product
  • 13. Potential Energy
  • 14. Application of Energy Conservation
  • 15. Mechanical Energy and the Simple Harmonic Oscillator
• Momentum

  • 16. Momentum and Impulse
  • 17. Systems, Center of Mass, and Conservation of Momentum
  • 18. Collision Theory
  • 19. Continuous Mass Flow
• Two-Dimensional Rotational Motion

  • 20. Two-Dimensional Rotational Kinematics
  • 21. Two-Dimensional Rotational Dynamics
  • 22. Torque and the Simple Harmonic Oscillator
  • 23. Static Equilibrium
• Angular Momentum

  • 24. Angular Momentum
  • 25. Conservation of Angular Momentum
• Rotation and Translation

  • 26. Two-Dimensional Rotation and Translation Kinematics
  • 27. Two-Dimensional Rotation and Translation Dynamics
• Central Force Motion

  • 28. Central Force Motion and the Kepler Problem
• Download Course Materials

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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

Notes: Simple Harmonic Motion (PDF - 3.8MB)

Suggested Textbook Reading (Optional)

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

Learning Activities

Guided Activities

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

Slides: Mechanical Energy and the Simple Harmonic Oscillator (PDF - 1.3MB)

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

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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

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/mechanical-energy-and-the-simple-harmonic-oscillator/help-session-9/GMYPQ-1l-d0.srt'}

Related Resources

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

• Try out the pendulum lab interactive simulation from PhET.
• Do the lesson on simple harmonic motion from the University of Tennessee web-based Physics course.
• Read about the simple harmonic oscillator from Prof. Daniel A. Russell at Kettering University.

 

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