Session Overview
Covered this week: Piano strings are each chosen and tuned such that they have a specific natural frequency. Image courtesy of Maruku San 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 25: Modal Analysis: Response to IC's and to Harmonic Forces
Lecture 25: Modal Analysis: Response to IC's and to Harmonic Forces
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Video Chapters
- Outline of the final three lectures
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Response to initial conditions and the use of Rayleigh damping to model modal damping ratios
Response to initial conditions and the use of Rayleigh damping to model modal damping ratios
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Steady state response to harmonic excitation by the method of modal analysis
Steady state response to harmonic excitation by the method of modal analysis
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Demonstration of the response of a string to harmonic excitation
Demonstration of the response of a string to harmonic excitation
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Demonstration of the response of a string to initial deflection
Demonstration of the response of a string to initial deflection
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Direct method for assembling the stiffness of an N DOF system
Direct method for assembling the stiffness of an N DOF system
> Download from iTunes U (MP4 - 253MB)
> Download from Internet Archive (MP4 - 253MB)
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Video Chapters
- Watch
Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions
Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
- Video Chapters
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Discussion of problem set concept questions
Discussion of problem set concept questions
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
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Review of the use of a transfer function to analyze the response of a single DOF system to harmonic input
Review of the use of a transfer function to analyze the response of a single DOF system to harmonic input
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
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Analysis of the response of a 2-DOF system to harmonic excitation by means of transfer functions and the introduction of the application of the dynamic absorber to mitigate problem vibration
Analysis of the response of a 2-DOF system to harmonic excitation by means of transfer functions and the introduction of the application of the dynamic absorber to mitigate problem vibration
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
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Demonstration of a dynamic absorber using a strobe and a vibrating beam
Demonstration of a dynamic absorber using a strobe and a vibrating beam
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
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Questions and answers: discussion of helicopter video and the 300 ton dynamic absorber in the Hancock building
Questions and answers: discussion of helicopter video and the 300 ton dynamic absorber in the Hancock building
> Download from iTunes U (MP4 - 263MB)
> Download from Internet Archive (MP4 - 263MB)
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Discussion of problem set concept questions
- Video Chapters
- Watch
Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc.
Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc.
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
- Video Chapters
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Demonstration of wave propagation on a long string
Demonstration of wave propagation on a long string
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
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My personal research area: Flow-induced vibration of long strings and beams in fluid flow
My personal research area: Flow-induced vibration of long strings and beams in fluid flow
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
- Derivation of the wave equation
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Natural frequencies and mode shapes of the string under tension-with demonstration
Natural frequencies and mode shapes of the string under tension-with demonstration
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
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Application of the wave equation to rods, organ pipes, shower stalls with demonstrations
Application of the wave equation to rods, organ pipes, shower stalls with demonstrations
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
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The vibration of beams: natural frequencies as a function of boundary conditions, dispersion in wave propagation
The vibration of beams: natural frequencies as a function of boundary conditions, dispersion in wave propagation
> Download from iTunes U (MP4 - 229MB)
> Download from Internet Archive (MP4 - 229MB)
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Demonstration of wave propagation on a long string
- Video Chapters
Recitation Video and Notes
- Watch
Recitation 12: Modal Analysis of a Double Pendulum System
Recitation 12: Modal Analysis of a Double Pendulum System
> Download from iTunes U (MP4 - 167MB)
> Download from Internet Archive (MP4 - 167MB)
- This recitation takes an in depth look at modal analysis for a double pendulum system.
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Recitation 12 Notes: Modal Analysis (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 11: Concept Question Answer Key (PDF)
- Problem Set 11: Problem Solutions and Explanations (PDF)