Session Overview
Covered this week: The ripples on this pond are an example of superposed waves that will soon disperse. Image courtesy of John Martin on Flickr. |
Assignments
Problems and Concept Questions
Each problem set has concept questions paired with most problems. Answers to the concept questions are handed in before the overall problem set is due. You should therefore answer the concept questions in each problem set while watching the video lectures for the week. Then, use the Concept Question Answer Key (below in the Check Yourself section) to check your work before continuing to work on the problem set.
Please note that if your answer to the concept question is incorrect, it is likely that you may start down an unproductive pathway to a solution. Try to fully understand the answer to the concept question before you begin the regular problem.
Videos
Lecture Videos
- Watch
Lecture 23: Vibration by Mode Superposition
Lecture 23: Vibration by Mode Superposition
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
- Video Chapters
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Review of the concept questions with Homework 10
Review of the concept questions with Homework 10
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
-
Overview of the vibration material to be covered in the course
Overview of the vibration material to be covered in the course
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
- Linearization of a 2-DOF system
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Free vibration of linear multi-DOF systems-intro to mode superposition
Free vibration of linear multi-DOF systems-intro to mode superposition
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
-
Finding natural frequencies and mode shapes of multi-DOF systems
Finding natural frequencies and mode shapes of multi-dof systems
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
-
Mode superposition analysis of a 2-DOF system
Mode superposition analysis of a 2-DOF system
> Download from iTunes U (MP4 - 251MB)
> Download from Internet Archive (MP4 - 251MB)
-
Review of the concept questions with Homework 10
- Video Chapters
- Watch
Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix
Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
- Video Chapters
- The modal expansion theorem
- Vibrating string demonstration
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Demonstration of modes with the 2 DOF mechanical model
Demonstration of modes with the 2 DOF mechanical model
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
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Orthogonality and the computation of the mass and stiffness matrices
Orthogonality and the computation of the mass and stiffness matrices
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
-
Response to initial conditions using modal analysis
Response to initial conditions using modal analysis
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
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Obtaining uncoupled equations of motion and determination of modal initial conditions
Obtaining uncoupled equations of motion and determination of modal initial conditions
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
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Dealing with damping in modal analysis
Dealing with damping in modal analysis
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
-
Rayleigh damping and experimental fitting of damping ratios
Rayleigh damping and experimental fitting of damping ratios
> Download from iTunes U (MP4 - 262MB)
> Download from Internet Archive (MP4 - 262MB)
- Video Chapters
Recitation Video and Notes
- Watch
Recitation 11: Double Pendulum System
Recitation 11: Double Pendulum System
> Download from iTunes U (MP4 - 131MB)
> Download from Internet Archive (MP4 - 131MB)
- This recitation introduces modal analysis and looks at a double pendulum problem.
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Recitation 11 Notes: Double Pendulum System (PDF)
- These recitation notes were compiled by Prof. David Gossard, another instructor for the course. His notes go over concepts and problems covered during the recitation sections he taught, and may not precisely correspond to the content covered in the above recitation video.
Check Yourself
Concept Question Answer Key and Problem Set Solutions
The solutions are presented in two files, one with the answers to the concept questions, and one with solutions and in-depth explanations for the problems. Work the problems on your own and check your answers when you're done.
- Problem Set 10: Concept Question Answer Key (PDF)
- Problem Set 10: Problem Solutions and Explanations (PDF - 1.1MB)
Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.