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
 Video Chapters
 Review of the concept questions with Homework 10
 Overview of the vibration material to be covered in the course
 Linearization of a 2DOF system
 Free vibration of linear multiDOF systemsintro to mode superposition
 Finding natural frequencies and mode shapes of multidof systems
 Mode superposition analysis of a 2DOF system
 Video Chapters

Watch Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix
 Video Chapters
 The modal expansion theorem
 Vibrating string demonstration
 Demonstration of modes with the 2 DOF mechanical model
 Orthogonality and the computation of the mass and stiffness matrices
 Response to initial conditions using modal analysis
 Obtaining uncoupled equations of motion and determination of modal initial conditions
 Dealing with damping in modal analysis
 Rayleigh damping and experimental fitting of damping ratios
 Video Chapters
Recitation Video and Notes
 Watch Recitation 11: Double Pendulum System
 This recitation introduces modal analysis and looks at a double pendulum problem.
 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 indepth 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.