# MIT-2.003SC Engineering Dynamics, Fall 2011

## Instructors

## Categories

## Course Description

## 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

### Physics Requirements

## Course Components and Requirements

This course consists of the following components:

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

### Lectures

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.

### Recitations

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

## Lectures in this course

1. Lecture 1 - History of Dynamics; Motion in Moving Reference Frames

2. Lecture 2 - Newton's Laws & Describing the Kinematics of Particles

3. Lecture 3 - Motion of Center of Mass; Acceleration in Rotating Ref. Frames

4. Lecture 4 - Movement of a Particle in Circular Motion w/ Polar Coordinates

5. R2 - Velocity and Acceleration in Translating and Rotating Frames

6. Lecture 5 - Impulse, Torque, & Angular Momentum for a System of Particles

7. Lecture 6 - Torque & the Time Rate of Change of Angular Momentum

8. R3 - Motion in Moving Reference Frames

9. Lecture 7 - Degrees of Freedom, Free Body Diagrams, & Fictitious Forces

10. Lecture 8 - Fictitious Forces & Rotating Mass

11. R4 - Free Body Diagrams

12. Lecture 9 - Rotating Imbalance

13. Lecture 10 - Equations of Motion, Torque, Angular Momentum of Rigid Bodies

14. R5 - Equations of Motion

15. Lecture 11 - Mass Moment of Inertia of Rigid Bodies

16. Lecture 12 - Problem Solving Methods for Rotating Rigid Bodies

17. R6 - Angular Momentum and Torque

18. Lecture 13 - Four Classes of Problems With Rotational Motion

19. Lecture 14 - More Complex Rotational Problems & Their Equations of Motion

20. R7 - Cart and Pendulum, Direct Method

21. Notation Systems

22. Lecture 15 - Introduction to Lagrange With Examples

23. R8 - Cart and Pendulum, Lagrange Method

24. Lecture 16 - Kinematic Approach to Finding Generalized Forces

25. Lecture 17 - Practice Finding EOM Using Lagrange Equations

26. R9 - Generalized Forces

27. Lecture 18 - Quiz Review From Optional Problem Set 8

28. Lecture 19 - Introduction to Mechanical Vibration

29. Lecture 20 - Linear System Modeling a Single Degree of Freedom Oscillator

30. Lecture 21 - Vibration Isolation

31. Lecture 22 - Finding Natural Frequencies & Mode Shapes of a 2 DOF System

32. R10 - Steady State Dynamics

33. Lecture 23 - Vibration by Mode Superposition

34. Lecture 24 - Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix

35. R11 - Double Pendulum System

36. Lecture 25 - Modal Analysis: Response to IC's and to Harmonic Forces

37. Lecture 26 - Response of 2-DOF Systems by the Use of Transfer Functions

38. Lecture 27 - Vibration of Continuous Structures: Strings, Beams, Rods, etc.

39. R12 - Modal Analysis of a Double Pendulum System