## 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)

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

Lecture Notes from class:

L2: Jan 28 - Motion of Particles. Accelerometer data Matlab codeL3Circular motion, normal-tangential and polar coordinates, Newton's lawsL4:Examples of using Newton's laws to calculate forces; trajectory equationsL5:Deriving and solving EOM with mupad and matlab. mupad file impeller.m springmass.mL6Examples using MATLAB: squirrel trajectories, earthquakes. squirrel.m building.

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

L7:Work, power, kinetic energy relations for a particleL8:Conservative forces, potential energy, conservative systems and applications of energy relations for conservative systemsL9:Linear impulse-momentum relations for particles, analyzing collisions between particlesL10Angular Momentum

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)

L11Features of vibrations, SHM, Free Vibration of undamped 1DOF systems (Harmonic Oscillator); Natural Frequencies and Mode ShapesL12Counting DOF and vibration modes; combining springs in series/parallel; relation between natural frequency and static deflection using energy methods to derive equations of motion for undamped 1DOF systemsL13Finding natural frequencies for nonlinear systems (pendulum, minus-k); damped vibrations (dashpot, EOM for damped spring-mass system; solution; discussion)L14Determining natural frequency and damping from an experimental measurement, Forced vibrations: EOM, transient and steady state solution, the magnification, discussion of amplitude-v-frequency response of forced systems.L15Finding natural frequency and damping from measured forced vibrations, Qualitative discussion of forced vibration of 2DOF systems; base excitation; examples of suspension design calculation.L16Vibrations caused by an unbalanced rotor; calculating natural frequencies for a simple 2 DOF system

Prof Bower's free vibration summary slides (from section) (ppt file)

Prof Bower's forced vibration summary slides (from section) (ppt file)

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) 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

L17: Kinematics of Rigid Bodies

L18:Kinematics examples; head accelerations; rolling disks Notes on rolling disks

L19:Moments of inertia, dynamics of rigid bodies

L20:Rigid body dynamics examples, kinetic energy

L21:Examples of calculating KE in systems of rigid bodies

L22:Angular Momentum

L23:Solar Car Project