Vibration Analysis by Mode Superposition

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Session Overview

Close up image of piano strings inside a piano.

Covered this week:
This week we apply modal superposition to the analysis of the response of multi-dof systems to initial conditions and to excitation by steady state harmonic forces.

Piano strings are each chosen and tuned such that they have a specific natural frequency. Image courtesy of Maruku San on Flickr.


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.


Lecture Videos

Recitation Video and Notes

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.


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