## 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)

**Class notes from lecture will be posted here** (note that the lectures are also recorded on lecture-capture - to access them go to the Canvas site for the course, and click the 'EchoCenter' button on the left - so you can find the explanations that went with the formulas in class if you need them)

- L2: Motion of particles - position,velocity acceleration relations, math review, straight line motion, integrating experimental measurements of acceleration using MATLAB matlab file from class, data file from class (the lecture capture failed for this class - sorry!)
- L3: Motion of particles - circular motion with normal/tangential coords; polar coords; Newton's laws, tablecloth example
- L4: Motion of particles - examples of F=ma and M_c=0; example of F=ma and n-t coordinates; calculating the path of a particle using Newton's laws; trajectory formulas
- L5 Motion of particles - calculating particle motion using F=ma and solving the differential equation with Mupad and Matlab. Centrifugal pump example and suspension example. Impeller matlab Spring-mass matlab

**Worked problems from Section**

- S4: Motion of Particles - Straight-line motion with variable acceleration; example using n-t coordinates; example using polar coordinates; example of F=ma and Mc=0 to calculate reaction forces

**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 lectures2.1 Forces

2.2 Moments

2.3 Force couples, pure moments and Torques

2.4 Constraint and reaction forces and moments

2.5 Friction forces

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 Solving equations of motion for systems of particles with MATLAB

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

4.2 Linear impulse-momentum relations

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

Summary of Solutions to EOM for vibration problems (pdf)

Java forced vibration simulator

(The Java Applets were written way back in the day when love was free, and the internet was innocent and trusting, and the word 'hacker' did not yet exist. Getting them to run on browsers with modern security features is a chore. You need to

(i) Download the latest Java (go to java.com);

(ii) Go to your computer security settings (Control Panel);

(iii) select Programs from the menu on the left and then click the Java icon;

(iv) select the Security tab from the top of the menu; click the 'Edit Site List' button;

(v) Click Add

(vi) Enter the web address of the Notes page of the course website into the box provided

http://www.brown.edu/Departments/Engineering/Courses/En4/Notes/notes.html

(vi) Move the Security bar to 'Medium'

(vi) Click OK.

(vii) Ignore the dire warning (taking this course might mess with your brain but we wont do anything to your computer)

You should then be able to run the applets. If any of you CS150 wizards have the interest, time, expertise and infrastructure to package our old Java codes into signed JAR files we would love to hear from you!

6. Analyzing motion of systems of rigid bodies6.1 Introduction to Rigid Body Motion

6.2 Describing (two dimensional) rigid body motion

6.3 Equations of motion for a rigid body moving in a plane

6.4 Solving equations of motion for a rigid body

6.5 Energy and Momentum for rigid bodies

6.6 Application to power transmission