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Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.
Part I: Mechanical Vibrations and Waves
Exam Information
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Exam one covers Lectures 1 through 8. |
What You Should Know:
- How to write down Equation of Motion
- Undamped, under-damped, critically damped, over-damped
- Driven oscillator, transient behavior and steady state solution, resonance
- How to determine the unknown coefficients using initial conditions
- Coupled systems: What are the normal modes? How to solve M-1K eigenvalue problems and what are the full solutions? Driven coupled oscillator, resonance
- Symmetry & Infinite coupled system: What is the solution of reflection and translation symmetric system? How to determine the dispersion relation ω(k)?
Practice Exam
Lecture Topics
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Lecture Video: Periodic Oscillations, Harmonic Oscillators
In this lecture, Prof. Lee discusses the mathematical description of the periodic oscillation and simple harmonic oscillators. The first 5 minutes are devoted to course information.
Lecture Notes
Typed Notes for Lecture 1 (PDF)
Handwritten Notes for Lecture 1 (PDF - 2.2MB)
Textbook Reading
Chapter 1: Harmonic Oscillation (PDF - 1.4MB)
Problem Set
Problem Solving Help Video*
Simple Harmonic Motion and Introduction to Problem Solving
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Air Cart Between Springs |
| Mass on a Spring |
| Two Pendulums with Different Amplitudes |
* Note: This Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Lecture Topics
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Lecture Video: Traveling Waves
Prof. Lee introduces the traveling wave solution of the wave equation. He also shows the string “remembers” the shape of the traveling wave though energy stored in the form of kinematic energy.
Lecture Notes
Typed Notes for Lecture 10 (PDF - 1.9MB)
Handwritten Notes for Lecture 10 (PDF - 2.4MB)
Textbook Reading
Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (section 6.2 to end)
Chapter 7: Longitudinal Oscillations and Sound (PDF - 1.3MB)
Chapter 8: Traveling Waves (PDF - 1.4MB) (through section 8.2)
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Bell Labs Wave Machine (Mismatched Impedance), Bell Labs Wave Machine (Mismatched Impedance), and Bell Labs Wave Machine (Mismatched Impedance) |
Lecture Topics
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Lecture Video: Sound Waves
Sound wave, a longitudinal wave, is discussed in this lecture. Prof. Lee calculates the speed of sound using two extreme cases: (1) constant temperature (2) adiabatic process. He also measures the speed of sound using an in-class demo.
Lecture Notes
Typed Notes for Lecture 11 (PDF - 1.2MB)
Handwritten Notes for Lecture 11 (PDF - 2.4MB)
Textbook Reading
Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (section 6.2 to end)
Chapter 7: Longitudinal Oscillations and Sound (PDF - 1.3MB)
Chapter 8: Traveling Waves (PDF - 1.4MB) (through section 8.2)
Problem Set
Problem Solving Help Video*
Electromagnetic Waves in a Vacuum
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Standing Sound Waves in a Glass Tube |
| Helium Balloon |
* Note: This Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Lecture Topics
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Lecture Video: Damped Free Oscillators
A more realistic physical system, a damped oscillator, is introduced in this lecture. Prof. Lee shows the mathematical solutions actually match the behavior of physical systems. He also does an in-class demo to compare damped and undamped oscillators.
Lecture Notes
Typed Notes for Lecture 2 (PDF)
Handwritten Notes for Lecture 2 (PDF - 2MB)
Textbook Reading
Chapter 2: Forced Oscillation and Resonance (PDF - 1.3MB)
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Oscillating Steel Ball on a Track, and Oscillating Steel Ball on a Track |
| Physical Pendulum |
| Damped and Undamped Masses on a Spring |
| Driven Torsional Balance Oscillator |
Lecture Topics
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Lecture Video: Driven Oscillators, Transient Phenomena, Resonance
Driven damped oscillators is the focus of this lecture. Prof. Lee shows the transient behavior, which looks completely chaotic at times, can be described by mathematics. He also discusses interesting phenomena such as resonance.
Lecture Notes
Typed Notes for Lecture 3 (PDF - 1.2MB)
Handwritten Notes for Lecture 3 (PDF - 2.1MB)
Textbook Reading
Chapter 2: Forced Oscillation and Resonance (PDF - 1.3MB)
Problem Set
Problem Solving Help Video*
Harmonic Oscillators with Damping
Coupled Oscillators without Damping
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Driven Cart on Air Track |
| Ball on String Pendulum |
| Driven Mechanical Oscillator |
| Breaking Glass with Sound |
Related Resources
Video: Pendulum Waves of Newton’s Cradle in motion set to music.
* Note: This Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Lecture Topics
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Lecture Video: Coupled Oscillators, Normal Modes
Prof. Lee analyzes a highly symmetric system which contains multiple objects. By physics intuition, one could identify a special kind of motion – the normal modes. He shows that there is a general strategy for solving the normal modes.
Lecture Notes
Typed Notes for Lecture 4 (PDF)
Handwritten Notes for Lecture 4 (PDF - 2.7MB)
Textbook Reading
Chapter 3: Normal Modes (PDF - 1.4MB)
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Double Pendulum |
| Weighted Hacksaw Blade |
| Two Rigid Pendulums Coupled with a Spring |
| Two Pendulums Coupled with a Rod |
| Wilberforce Pendulum and Wilberforce Pendulum |
Related Resources
Video: Normal Modes from PhET Interactive Simulations project at the University of Colorado Boulder
Lecture Topics
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Lecture Video: Beat Phenomena
Prof. Wyslouch shows the solution of two coupled pendula. A very interesting result from the calculation is that beat phenomena could be identified in the motion of the pendula, similar to what one could feel with sound waves.
Lecture Notes
Typed Notes for Lecture 5 (PDF - 1.1MB)
Handwritten Notes for Lecture 5 (PDF - 1.7MB)
Textbook Reading
Chapter 3: Normal Modes (PDF - 1.4MB)
Problem Set
Problem Solving Help Video*
Coupled Oscillators without Damping
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Two Rigid Pendulums Coupled with a Spring and Two Rigid Pendulums Coupled with a Spring |
| Wave Beats |
| Coupled Tunning Forks |
* Note: This Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Lecture Topics
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Lecture Video: Driven Oscillators, Resonance
Driving force is introduced in the coupled system. Prof. Wyslouch solves the system and he demonstrates that one could “excite” one of the normal modes by driving the system at the frequency it likes: normal mode frequency.
Lecture Notes
Typed Notes for Lecture 6 (PDF - 1.3MB)
Handwritten Notes for Lecture 6 (PDF - 1.5MB)
Textbook Reading
Chapter 4: Symmetries (PDF - 1.3MB)
Chapter 5: Waves (PDF - 1.4MB) (through section 5.2)
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Two Rigid Pendulums Coupled with a Spring |
| Coupled Air Carts |
Lecture Topics
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Lecture Video: Symmetry, Infinite Number of Coupled Oscillators
The mathematical description of “symmetry” is introduced. Prof. Lee shows that the concept of symmetry can be used to solve infinite numbers of coupled oscillators and that the sine waves we see in daily life are coming from translation symmetry.
Lecture Notes
Typed Notes for Lecture 7 (PDF - 1.1MB)
Handwritten Notes for Lecture 7 (PDF - 1.9MB)
Textbook Reading
Chapter 4: Symmetries (PDF - 1.3MB)
Chapter 5: Waves (PDF - 1.4MB) (through section 5.2)
Problem Set
Problem Solving Help Video*
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Bell Labs Wave Machine |
| Vibrating Spring (Hand Driven) |
* Note: These Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Lecture Topics
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Lecture Video: Translation Symmetry
Prof. Lee introduces the concept of “boundary conditions” which enables us to solve a finite system using the general solution of an infinitely long system. In the end of the lecture, a wave equation is derived in the continuous limit.
Lecture Notes
Typed Notes for Lecture 8 (PDF - 1.2MB)
Handwritten Notes for Lecture 8 (PDF - 1.9MB)
Textbook Reading
Chapter 5: Waves (PDF - 1.4MB) (section 5.3 to end)
Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (through section 6.1)
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Bell Labs Wave Machine |
Related Resources
Video: Wave on a String from PhET Interactive Simulations project at the University of Colorado Boulder
Lecture Topics
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Lecture Video: Wave Equation, Standing Waves, Fourier Series
The standing wave solution of the wave equation is the focus this lecture. Using a vibrating string as an example, Prof. Lee demonstrates that a shape can be decomposed into many normal modes which could be used to describe the motion of the string.
Lecture Notes
Typed Notes for Lecture 9 (PDF - 1.1MB)
Handwritten Notes for Lecture 9 (PDF - 1.7MB)
Textbook Reading
Chapter 5: Waves (PDF - 1.4MB) (section 5.3 to end)
Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (through section 6.1)
Problem Set
Problem Solving Help Video*
Traveling Waves without Damping
In-class Demonstrations
| SEE IT IN THE LECTURE |
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| Bell Labs Wave Machine and Bell Labs Wave Machine |
| Rijke Tube |
Related Resources
Video: Air Conditioner Noise by Prof. Yen-Jie Lee
Video: Intro to Fourier Series and How to Calculate Them by Dr. Chris Tisdell
Webpage: Fourier Series: Basics on OCW’s 18.03SC Differential Equations course
* Note: These Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.
Course Info
Learning Resource Types
theaters
Lecture Videos
notes
Lecture Notes
assignment
Problem Sets
Instructor Insights
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