# Engineering Analysis 3

**EA3 System Dynamics, Spring Quarter 2023**

Website: tinyurl.com/ea3nu

## Instructors, TAs, and Sections

- Section 21, 10-10:50 MWF, Tech M345; Tuesday, Tech M345
- Instructor: Prof. Kevin Lynch, kmlynch@northwestern.edu
- TAs:

- Section 20, 11-11:50 MWF, Pancoe Auditorium; Tuesday, Frances Searle 1421
- Instructor: Prof. Jeremy Keys, jeremy.keys@northwestern.edu
- TAs:

- Section 23, 1-1:50 MWF, Pancoe Auditorium; Tuesday, Annenberg G15
- Instructor: Prof. Cheng Sun, c-sun@northwestern.edu
- TAs:

- Section 22, 2-2:50 MWF, Pancoe Auditorium; Tuesday, Tech L211.
- Instructor: Prof. Sandip Ghosal, s-ghosal@northwestern.edu
- TAs:

TAs:

- Ayesha Ahmed, ayesha.ahmed1@northwestern.edu
- Caralyn Collins, CaralynCollins2024@u.northwestern.edu
- Shizhou Jiang, shizhou.jiang@northwestern.edu
- Shuting Lai, ShutingLai2023@u.northwestern.edu
- Haklae Lee, haklae.lee@northwestern.edu
- Rui Li, ruili2024@u.northwestern.edu
- Asma Meem, asmameem2026@u.northwestern.edu
- Nibir Pathak, NibirPathak2021@u.northwestern.edu
- Dono Toussaint, DonoToussaint2027@u.northwestern.edu

## Course Summary

EA3 focuses on the modeling of dynamic systems, the reduction of models to differential equations of motion, and some exploration of the system behavior relating to the solution of those equations.

The goal is to learn system modeling across disparate physical domains (mechanical, electrical systems). We will typically proceed using the following steps:

- to understand the elements of each domain (e.g. spring, capacitor; or force, voltage)
- to express precisely the way in which the elements interact (e.g. free-body diagrams, circuit diagrams)
- to reduce the idealized systems to equations
- to understand the behavior of the system by solving equations

There will be a strong emphasis on understanding how physical processes are described by mathematical equations.

## Course Policies

**Supportive Class Environment**

All members of this class (instructors, TAs, students) are expected to contribute to a respectful, inclusive, and supportive environment for every other member of the class.

We are all *partners* in your education; help us help you get the most out of this class. Please engage during class meetings.

**Honor Code**

You are encouraged to discuss the material with the instructor, course assistants, and your classmates, but you are not allowed to copy answers or code or share your answers or code with others. *Anyone copying answers or code, or providing answers or code, or becoming aware of others doing so without reporting to the instructor, is in violation of the honor code.*

**Academic Support and Learning Advancement (ASLA)**

Northwestern's Academic Support and Learning Advancement office offers peer-guided study groups, drop-in peer tutoring, individual and group peer academic coaching, and consultations to help students navigate their academic paths and refine their study strategies.

## Grading

Three quizzes count for 90% of your class grade. Homeworks account for the remaining 10%. Each quiz is in class (50 minutes). Students must attend the quiz in their own section, and the quizzes in each section will be different. Grades are assigned in each section independently of the other sections. There is no final exam during finals week.

## Homework

Assignments must be submitted electronically through Canvas. Late assignments are not accepted. No exceptions, so please don't ask. Your lowest homework grade will be dropped from the calculation of your homework score.

## Syllabus and Web Textbook

### General Introduction

**The Big Picture**: the EA3 three-step process, and what you will learn

### Mechanical Systems

**Mechanical systems and dampers**: assumptions, parameters vs. dynamic variables, dampers, across and through variables, constitutive law of the damper**Springs**: constitutive law, displacement and relaxed length, sign conventions, series and parallel**Formulating equations of motion for spring-damper systems**: step 1a) force balance at connections; step 1b) geometric continuity; elements in parallel and series; step 1c) constitutive laws; step 2 forming differential equations of motion**Step 3 solving equations of motion****Masses**: free body diagrams and force balance, sign convention, step 1 governing equations, step 2 state variables and state equations, obtaining state equations- Example: free body diagram and force balance
- Example: sign conventions
- Obtaining state equations: example 3, example 4, example 5, example 6, example 7, example 8, example 9, example 10

**Newtonian mechanics**: Newton's laws: Newton's laws, velocity and acceleration, center of mass, friction- Newton's laws example 1, example 2, example 3
- Velocity and acceleration example 4, example 5, example 6
- Friction example 8, example 9, example 10, example 11

**System dynamics and momentum conservation**: momentum and impulse, conservation of momentum, impacts- Momentum and impulse example
- Conservation of momentum projectile example
- Impacts: cars colliding example

**System dynamics and mechanical energy equation**: principle of work and energy, mechanical energy equation, energy stored in springs and dissipated in dampers- Mechanical energy equation example 1, example 2, example 3, example 4
- Energy stored in springs and dissipated in dampers: bungee jumper example

**Transformers**: levers, work, and power**Step 3 numerical solution of coupled differential equations**: state variables vs. parameters, initial conditions, evolution of spring-mass systems, forward Euler (non-matrix form), forward Euler (matrix form), MATLAB code**Step 3 (cont.) analytic solution of coupled differential equations**: analytic solutions, natural vibrations with damping, forced vibrations with no damping, free fall, complex numbers, superposition of solutions

### Electrical Systems

**Introduction**: voltage and current, charge and current, voltage and potential, power source: batteries**Resistors**: constitutive law (Ohm's law), meter polarities, power, Kirchoff's laws**Capacitors**: charge, capacitance, and energy**Formulating equations for circuits**: circuit diagram notation, Kirchoff's laws, step 1 equations, step 2 state variables and equations**Simple RC circuits**: RC time constant, charging up a capacitor- Example: RC time constant

**Complex RC circuits****Inductors**(applet broken)**Circuits with inductors**

### Reference

**Important concepts and formulas****Famous scientists****Mode analysis**- Example 1
- Example 2
- Example 3