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About this Course

This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.

Prerequisites and Preparation

In order to take this course at MIT, students are expected to be comfortable with the material from the following subjects:

Math Requirements

18.01SC, 18.02SC, 18.03SC

Physics Requirements


Course Components and Requirements

This course consists of the following components:

  • Lectures
  • Recitations
  • Problem Sets and Readings
  • Quizzes and Exams


Two lectures will be given each week. There will be physical and computational demonstrations in some of the lectures. Each lecture will be associated with a reading from the text. It is recommended that the students have read the assigned reading before lecture.

Videos of the twice-weekly lectures are provided. Each lecture can be viewed either as a whole, or you can jump to particular points in the lecture video by clicking on the concept links below the lecture.


At MIT, the class is divided up into smaller sections that meet once a week. In the recitation sections, which meet after students have gone to both lectures, the professors work through problems that incorporate the concepts presented that week.

The purpose of the recitations is to give students experience in the subject by working out examples and expanding on the material presented in the lectures. Attendance and participation in the recitations is expected and is factored into the final grade as explained below.

Videos from one of Prof. Vandiver's recitation sections are provided. As with the lecture videos, you can view the recitation either as a whole, or jump to particular places within the recitation using the links provided.

Recitation notes written by Prof. David Gossard, who leads another recitation section, are also provided.

Problem Sets and Readings

Problem sets consist of full problems and concept questions, which are multiple choice questions associated with the problems. Students should answer concept questions before completing the longer problems.

The concept questions are meant to encourage students to think about the problems early on and to give the staff an early indication of what material students find difficult. The concept questions must be an entirely individual effort.

Discussing the full problems with fellow students is encouraged, as this is a great way to gain a better understanding of the material. However, please attempt the problems individually before doing so. The work that you submit should reflect your own understanding of the problems and should not be copied. Please write down the names of your collaborators on the top of your homework.

Problem set grading is intended to reward earnest effort in mastering the course material without causing stress associated with attempts to achieve perfection. As a result, problem sets will not be corrected by graders nor awarded points on the basis of perfection. They will instead be graded P/D/F. Solutions will be posted in timely fashion. A "P" represents an earnest effort that demonstrates competence of physical and mathematical principles. "D" work is characterized by minimal effort and little awareness of the appropriate principles. An "F" is given for homework that shows no effort, has been copied from prior years' solutions, or is turned in late without prior approval from your recitation instructor.

There are no required textbooks for this course, but suggested readings are drawn from the following texts:

  • [Hibbeler]= Buy at Amazon Hibbeler, Russell C. Engineering Mechanics: Dynamics. 12th ed. Prentice Hall, 2009. ISBN: 9780136077916.
  • [Williams]= Buy at Amazon Williams, J. Fundamentals of Applied Dynamics. John Wiley & Sons, 1995. ISBN: 9780471109372.

Quizzes and Exams

During the course, students take two quizzes and one final exam. Both quizzes and the final will be closed book. One sheet (8.5 by 11 inches, front and back) of handwritten notes will be allowed at the first quiz, two sheets at the second quiz, and three sheets at the final exam.


At MIT, the grading for this class was broken down as follows:

Recitation participation 10%
Homework: concept questions 5%
Homework: full problems 10%
Quiz 1 20%
Quiz 2 25%
Final exam 30%

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