Course Description

University of California, Davis
Department of Mechanical and Aerospace Engineering
Introduction to Mechanical Vibrations - ENG 122
Winter 2020, Lecture: MW 10:00AM-11:50AM, Bainer Hall 1130
CRN: 77345

Mechanical structures and systems are susceptible to vibrations, i.e. periodic changes in the physical state. Vibrations can both be a hindrance and a benefit to machines. In this course, we will learn how one can predict vibrations and interpret both simulated and measured vibrations using analytical and computational means. We will cover topics ranging from free and forced vibrations in lumped-parameter systems with and without damping, vibrations in coupled systems, electromechanical analogs, and use of energy conservation principles.

Catalog Description

Lecture—4 hours. Prerequisite: C- or better in Engineering 102; C- or better in Engineering 6 or course 5 or Computer Science Engineering 30; ability to program in MATLAB. Free and forced vibrations in lumped-parameter systems with and without damping; vibrations in coupled systems; electromechanical analogs; use of energy conservation principles. GE credit: SciEng | QL, SE.—F. (F.)

Learning Objectives

There are three broad learning objectives that we focus on in the course:

  1. Students will be able to analyze vibrational measurement data to draw conclusions about the measured system's vibrational nature and describe how the system behaves with respect to vibration concepts.
  2. Students will be able to create simple mathematical and computational models of real vibrating systems that can be used to answer specific questions about the system by concisely demonstrating the vibrational phenomena.
  3. Students will be able to design a mechanical system that has desirable vibrational behavior.

Students that master these three core learning objectives will be well prepared to use mechanical vibration concepts, theories, and tools to solve engineering problems.


  • ENG 102
  • EME 5[*], ENG 6 or ECS 30
  • Ability to program in Matlab or similar language.
[*]Note that the course catalog incorrectly lists ENG 5 as an optional prerequisite. It should be EME 5.


Jason K. Moore
2095 Bainer Hall

Gregory Bales

Time and Location

The lecture/discussion meets on Mondays and Wednesdays from 10:00-11:50 AM in Bainer Hall 1130.

If you have any conflicts with the schedule, especially for the exam period, you must tell me in the first week of class (emergencies will be the only exception).

Office Hours

Jason's Office Hours
Location: Bainer 2095
Time: Wednesdays 1:10 PM to 2:00 PM (shared with EME 171), Thursdays 2:10 PM to 3:00 PM

Greg's Office Hours
Location: Bainer 2071
Time: Thursday's 1PM-2PM and Friday's 11AM-12PM

If it is impossible to make office hours, schedule an appointment with Jason by checking his work calendar and select a free time between 8:00 AM and 6:30 PM Monday-Friday. Send him an email requesting an appointment at the suggested meeting times at least two days in advance. You can also email Kenny and request a meeting.

Academic Integrity

Academic dishonesty will not be tolerated. Please visit the Academic Integrity web page from UC Davis Office of Student Judicial Affairs to review the campus' policy on academic responsibility and integrity and read the UC Davis code of academic conduct.

Feel free to discuss homework assignments and work on them together, but each student must turn in a unique solution and presentation of the work. Keep in mind that actually doing all of the homework yourself is critical for learning and passing the course.

You may discuss your projects with others but the presented text, code, figures, and other materials in the reports must be created solely by yourself.


There is no assigned textbook for the course but you may want to obtain a mechanical vibrations textbook for reference. There are numerous books on the subject that all present essentially the same materials. Here are some options:

Mechanical Vibrations, J.P. Den Hartog
This is the first an most widely read book on the subject. For those that want the classic perspective.
Engineering Vibration, Daniel J. Inman, 4th Edition, Pearson Education.
Book that was used for this course in the recent past.
Mechanical Vibrations, Singiresu S. Rao, 2016
Highly cited text.
Mechanical Vibrations: Theory and Applications, Tse, Morse, and Hinkle, 1978
PDF download
Mechanical Vibrations, Anil V. Rao, 2009, (130 pages)
Lecture notes for course EME 4220 at the University of Florida.
Mechanical Vibrations, D.E. Adams (131 pages)
Notes from Prof. Adam's course ME 563 at Purdue.
Mecanical Vibrations, Luis San Andres, 2008
Notes from Texas A&M's course.
Vibration, Wikipedia Authors

Assignments & Grades

Grades will be available in the grade book periodically throughout the course along with class statistics. Check the website on a regular basis to gauge your performance. Keep in mind that 15% is deducted per business day late on all assignments except for the final report in 100% will be deducted if late.

Classwork 10%
Homeworks 30%
Midterm Project Report 20%
Final Project Report 30%
Final Project Presentation 10%
There will be a large number of in class computational exercises. These will be graded for participation and/or correctness. You may have to finish the activities we started in class outside of class and submit with your homework that week.
Weekly homework will be assigned which will be due before class the following week.
You will select a course project from a set of options provided by the instructors or one that you choose yourself. Approximately, midway through you will turn in a midterm report detailing a model that you develop for your system. At the end of the course, you will submit a report and give a 5 minute lightning talk during the scheduled exam period detailing the modeling, analysis, and design aspects of your project.


We will make use of Canvas for the course. Log in to with your Kerberos ID and passphrase then select ENG 122 001 WQ 2020.

We will be using several features in canvas:

This will be the instructors' primary communication avenue to you. These announcements will be forwarded automatically to your UCD email address. You are expected to read these either through your email program or on the Canvas website.
The electronic assignments will be listed here but will be distributed and collected through the JuyterHub.
Canvas discussions should be used for all questions about the class, homework, theory, projects, etc that is not of a private nature. Discussions allows both the instructors and students to collectively answer questions for the whole classes benefit. When considering contacting the instructors via email you should default to submitting it via Discussions unless the question is a private matter.
Your grades and basic stats on your relative performance will be available as the course goes along.
Copyrighted and private files, documents, and other resources will be available here for download. The rest will be available for download on this website.


The primary instructor should be informed of any learning accommodations at least 1 full week before the desired accommodation is needed. I expect students to contact me to discuss any special arrangements with 1 week time to make and agree on the arrangements.


All of the in-class exercises will be done on a personal computing device (preferably one with a keyboard) that you will be expected to bring to class. If you do not have a suitable computing device that you can bring to class, you will need to let the primary instructor know the day of the first class period.

Student Campus Resources

This is a helpful page for students' frequently asked questions: