## Syllabus and Lecture Notes

**Course Goals: on completing EN0040, students will:**

- Be able to idealize a simple mechanical system or component as a collection of particles or rigid bodies, and to use Newtonian mechanics, with the aid of analytical or computational methods, to analyze forces and motion in the idealized system. Relates to ABET outcomes (a), (e), (k)
- Be familiar with the characteristics of vibrations in linear systems; and have the ability to analyze the free, damped, and forced vibrations of a 1 degree of freedom system. Relates to ABET outcome (a)
- Be able to design and conduct simple experiments to measure the dynamical properties of a mechanical system or components. Relates to ABET outcome (b)
- Be able to apply Newtonian mechanics to design a mechanical system to meet specified constraints, including: to function effectively in teams of 3-5 students; to communicate design specifications through clear and effective oral and written reports, to perform appropriate design calculations and optimization where appropriate, and to successfully manufacture and test a completed design Relates to ABET outcome (a), (b), (c), (g)

**Workload Expectation**

- Lectures: 23x80 mins = 31 hours
- Conference Sections 24x50 mins = 20 hrs
- Homework assignments: 8 at 8 hours each = 64 hrs
- Projects: 4 at 10 hours each
- Midterm exam: 80 mins in class, plus 10 hours preparation
- Final exam, 3 hours (as scheduled by Registrar) plus 15 hrs preparation

**TOTAL: **185 hours.

(Explanation: this represents a rough estimate of the time spent by an average student on the class. Your actual workload may be less or greater than the estimate (projects are open ended and the time commitment depends on how many candidate designs you develop and their complexity; we also drop the lowest homework grade so some people only submit 7 homeworks) . Federal regulations require 4 credit classes to exceed 180 hours)

**Notes from Lecture (9am Tu/Th). See also lecture capture on Canvas - go to Media Library**

- pdf copies of notes from lecture and Section will be posted here

**Detailed notes (electronic text)**

1. Brief introduction to the objectives and methods of dynamics

2. Review of forces and Moments (pdf version) (reading assignment - not covered in lectures2.3 Force couples, pure moments and Torques

3. Analyzing motion of systems of particles(pdf version)3.1 Equations of motion for a particle

3.2 Calculating forces required to cause prescribed motion of particles

3.3 Deriving and solving equations of motion for systems of particles

4. Conservation Laws for Particles(pdf version)4.1 Work, power, potential energy and kinetic energy relations

4.2 Linear impulse-momentum relations

5. Vibrations(pdf version)5.1 Features of vibrations and overview of issues in controlling vibrations

5.2 Free vibration of conservative single degree of freedom systems

5.3 Free vibration of damped single degree of freedom systems

5.4 Forced vibration of single degree of freedom systems

5.5 Solving differential equations for vibrating systems (for reference - not covered in lectures)

5.6 Introduction to vibration of multi-degree of freedom systems (advanced topic - not covered in lecture)

Summary of Solutions to EOM for vibration problems (pdf)

J

ava vibration demonstrationsThese will only run in Microsoft Internet Explorer - you can use the IE plugin to run them in Chrome or Firefox - and need to be added to the Site Exception List in your Java control panel to run. You can find additional instructions to set this up here.

Cut and paste the links below into the IE address bar in an Internet Explorer window

Free Vibration Simulator: http://www.brown.edu/Departments/Engineering/Courses/En4/java/free.html

Forced Vibration Simulator: http://www.brown.edu/Departments/Engineering/Courses/En4/java/forced.html

6. Analyzing motion of systems of rigid bodiespdf version - (see the html for the animations)6.1 Introduction to Rigid Body Motion

6.2 Describing Motion of a Rigid Body (rotation tensor; angular velocity and acceleration)

6.3 Analyzing Motion in Connected Rigid Bodies (mechanisms, rolling wheel, gears)

6.4 Linear Momentum, Angular Momentum and KE of rigid bodies (calculating COM and Inertia)

6.5 Rotational Forces: Review of moments exerted by forces and torques

6.6 Dynamics of rigid bodies (equations relating forces and moments to motion)

6.7 Summary of equations of motion for rigid bodies (long list of all important equations)

6.8 Examples of solutions to problems involving motion of rigid bodies