## 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 6 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**

- Jan 26 Intro lecture (org slides only for copyright reasons - see Lecture Capture for the full presentation)
- Jan 31 L2: Particle Dynamics - r-v-a relations; calculus review; straight line motion examples. MATLAB code, datafile.
- Feb 2 L3: Particle Dynamics circular motion, normal/tangential and polar coords, Newton, tablecloth trick
- Feb 7 L4: Particle Dynamics examples of F=Ma and Mc=0, F=ma with n-t coords, trajectory equations
- Feb 9 L5: Particle Dynamics - analyzing motion with Mupad/Matlab Mupad script Impeller matlab Spring-mass matlab
- Feb 14 L6: Particle Dynamics - Squirrels; ''event' function; Building vibration, Squirrel MATLAB, building MATLAB
- Feb 16 L7 Power-Work-Energy relations for a particle;
- Feb 23 L8 Conservative forces, potential energy, energy conservation equation for a conservative system
- Feb 28 L9: Linear Impulse-momentum relations for particles
- Mar 2 L10: 3D collisions, Angular Impulse-Momentum equations for particles
- Mar 7: L11Vibrations of free undamped 1-DOF systems
- Mar 14: L12 Vibrations of undamped 1-DOF systems - counting DOF; series/parallel springs; energy method for EOM
- Mar 16 L13 Natural frequencies of nonlinear systems; damped vibrations (dashpots, solutions for damped system)
- Mar 21: L14 Damped vibration example, measuring wn and zeta from damped vibes, forced vibrations I
- Mar 23: L15 Forced vibrations: discussion of forced spring/mass system, base and rotor excitated systems.
- April 4: L16 Rigid Bodies: Describing rotations - rotation tensor, angular velocity and acceleration vectors
- April 6: L17 Rigid Bodies: Spin tensor, rigid body kinematics formulas, analyzing motion in mechanisms
- April 11: L18 Rigid Bodies: Gears, pulleys and the rolling wheel; angular momentum and KE for systems of particles
- April 13: L19 Inertial properties of rigid bodies, KE and angular momentum for 2D solids, parallel axis theorem Mupad
- April 18 L20 2D Dynamics of rigid bodies: solving problems with linear and angular momentum formulas
- April 19 L21 2D Dynamics of rigid bodies: wheel with sliding contact; fixed axis rotation problems; energy methods
- April 25 L22 3D Dynamics of rigid bodies: angular momentum methods, precession, matlab for free spinning block
- April 27 L23 Solar Car Project

**Summary Slides for Final (also available as large ppt file for the animations)**

**Notes from Section (9am/10am MW - Prof Bower)**

- Jan 25: slides Matlab script MATLAB vectors, matrices, loops, conditionals, functions:
- Jan 30: slides Mupad script Matlab script Euler method demo Matlab functions, solving ODEs with mupad and matlab:
- Feb 6: slides straight line motion with variable a, examples of n-t coordinates and polar coordinates
- Feb 13: Slides Matlab for quadrupole filter, mupad for chaotic pendulum, matlab for chaotic pendulum
- Feb 22 Matlab Optimizers matlab demo code
- Feb 27 Work, Power, Energy and Energy conservation examples. Mupad for atomic potential calculation
- March 6: Angular momentum, energy (Baby walker, Rutherford scattering)
- March 13: Vibrations I: Calculating natural frequencies for conservative 1 DOF systems
- March 20: Vibrations II: counting DOF; getting EOM with energy; damped free vibrations
- April 3: Forced Vibrations
- April 17: Rigid Bodies: 9am Section Mupad for Ig calculation 10am Section (the two covered different examples)
- April 24: Rigid body dynamics

**Notes from Section (1pm/2pm MW - Prof Xu)**

- Jan 30: Solving ODEs with mupad and matlab: slides Matlab script

**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)

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

6.7 Examples of solutions to problems involving motion of rigid bodies