Engineering Analysis 3

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EA3 System Dynamics, Spring Quarter 2023

This wiki page:

Instructors, TAs, and Sections

Each section covers the same material, at approximately the same pace, following the same readings from the web textbook (below), though each instructor's lecture notes and teaching style may be different. All sections have the same homeworks, due the same time and day. The quizzes in each section will be different.

  • Section 21: Lecture 10-10:50 MWF Tech M345; TA-led discussion Tuesday, Tech M345
    • Instructor: Prof. Kevin Lynch,
    • TAs: Nibir Pathak,; Dono Toussaint,
  • Section 20: Lecture 11-11:50 MWF Pancoe Auditorium; TA-led discussion Tuesday, Frances Searle 1421
    • Instructor: Prof. Jeremy Keys,
    • TAs: Ayesha Ahmed,; Haklae Lee,
  • Section 23: Lecture 1-1:50 MWF, Pancoe Auditorium; TA-led discussion Tuesday, Annenberg G15
    • Instructor: Prof. Cheng Sun,
    • TAs: Caralyn Collins,; Shizhou Jiang,
  • Section 22: Lecture 2-2:50 MWF, Pancoe Auditorium; TA-led discussion Tuesday, Tech L211
    • Instructor: Prof. Sandip Ghosal,
    • TAs: Shuting Lai,; Asma Meem,





Office Hours

Office hour schedule, beginning April 3. All office hours in Tech AG21 unless otherwise noted.
9-10 am 10-11 am 11-12 pm 12-1 pm 1-2 pm 2-3 pm 3-4 pm 4-5 pm 5-6 pm
Mon Lee Lee
Tues Keys, Tech L494 Jiang Jiang
Wed Meem Meem Sun Collins Collins Lynch (canceled May 31)
Thurs Ahmed Ahmed Lai Lai
Fri Pathak Pathak Toussaint Toussaint Ghosal, Tech L495

Course Summary

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

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

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

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

Prerequisite: a C- or better in EA2.

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 from others in the class or any other sources, nor are you allowed to 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.

Accessible NU

If you need accommodation in this course because of a disability, contact Accessible NU immediately.

Course Schedule and Quizzes

Lectures MWF by the instructors. Tuesday discussion sections led by the TAs, primarily focused on solving problems. First day of class is Tuesday March 28, but following a Monday schedule. We begin the normal rhythm Wednesday March 29. Office hours begin Monday April 3, and the first homework is due Thursday April 6.

There will be three in-class 50-minute quizzes, on

  • Monday April 24
  • Monday May 15
  • Friday June 2 (last day of class)

Students must attend the quiz in their own section, and the quizzes in each section will be different. There is no final exam. No electronic devices (phones, tablets, laptops, watches, etc.) are allowed during quizzes. No notes or scratch paper.

Quizzes focus mostly on recent material (e.g., material not covered on previous quizzes), but they may require anything from the course up until the most recent homework.

Partial credit may be awarded, so make sure your thought process is clear in your answer. If you just write an answer, and it is wrong, you will get no credit. If you just write an answer, and it is correct but it is not obvious to us where the answer came from, you may not get credit. We strive for consistency in awarding partial credit, so requests for more partial credit will not be considered. The only way to ensure full credit is to get the answer correct and to be clear about how you arrived at it.

If you think there was an error grading your quiz, you may request a regrade by typing a clear explanation and turning it in, along with the quiz itself, to an instructor at the next class after the quiz was returned to you. If a regrade is requested, your score may go up or down on any question on the quiz. No marks, erasures, or alterations to the quiz, of any kind, are allowed. Regrades may only be requested if there was an error in grading; requests for more partial credit will not be accepted.

If you are registered with Accessible NU for a testing accommodation, and you are in the 10:00, 11:00, or 1:00 sections, report to the following rooms at your normal class time on days of quizzes:

  • Monday April 24: the Hive (Ford building, just after the 2nd floor bridge from Tech)
  • Monday May 15: Tech C211
  • Friday June 2: Tech C211

If you are in the 2:00 section, you will take your April and May quizzes in your normal Pancoe lecture hall. On June 2, you will go to Tech C211.


Homeworks are due each Thursday at 5 PM, and homework solutions will be released Thursday nights. Homeworks must be submitted electronically through Canvas. Late assignments will not be accepted. No exceptions, so please don't ask. Your lowest homework grade will be dropped from the calculation of your homework score.

Homework must be submitted in a single pdf file, titled LastnameFirstname.pdf (substitute in your own last name [family name] and first name [given name]). All work must be clear and legible or you will not receive full credit. Make sure to show your thought process in case multiple steps are involved; don't just give an answer. Some homeworks involve Matlab programming. You should comment your code so it is easy to understand.


The three quizzes count for 90% of your class grade. Homeworks account for the remaining 10%. Test scores and final grades are assigned in each section independently of the other sections. So if your homework and test score average in section A is 75% and your friend's in section B is 85%, your friend's final grade will not necessarily be higher than yours.

Because of the large size of the course, make-up quizzes are not offered. Your lowest quiz score will be dropped when calculating your course quiz score. So if you need to miss a quiz because of sickness, an emergency, etc., or you just do poorly on one of your three quizzes, that quiz score will be dropped in calculating your grade. If you have two emergencies during the quarter and need a further accommodation, we will direct you to the undergraduate engineering office so you can get the accommodation you need.

Syllabus and Web Textbook

The "book" for this course is the web textbook, below.

Week 1

General Introduction

Mechanical Systems

  1. Mechanical systems and dampers: assumptions, parameters vs. dynamic variables, dampers, across and through variables, constitutive law of the damper
  2. Springs: constitutive law, displacement and relaxed length, sign conventions, series and parallel
    1. Example: which are springs?
    2. Example: total stiffness of a system

Week 2

  1. 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
    1. Examples: step 1a) force balance at connections example 1, example 2
    2. Examples: step 1b) geometric continuity example 3, example 4
    3. Examples: elements in parallel and series example 5, example 6
    4. Examples: forming differential equations of motion example 7, example 8
  2. Step 3 solving equations of motion
    1. Examples: what makes it a diffeq?, initial conditions, forward Euler method, analytical solutions
    2. Better numerical algorithms for differential equations

Week 3

  1. Masses: free body diagrams and force balance, sign convention, step 1 governing equations, step 2 state variables and state equations, obtaining state equations
    1. Example: free body diagram and force balance
    2. Example: sign conventions
    3. Obtaining state equations: example 3, example 4, example 5, example 6, example 7, example 8, example 9, example 10
  2. Newtonian mechanics: Newton's laws: Newton's laws, velocity and acceleration, center of mass, friction
    1. Newton's laws example 1, example 2, example 3
    2. Velocity and acceleration example 4, example 5, example 6
    3. Friction example 8, example 9, example 10, example 11

Week 4

  1. System dynamics and momentum conservation: momentum and impulse, conservation of momentum, impacts
    1. Momentum and impulse example
    2. Conservation of momentum projectile example
    3. Impacts: cars colliding example
  2. System dynamics and mechanical energy equation: principle of work and energy, mechanical energy equation, energy stored in springs and dissipated in dampers
    1. Mechanical energy equation example 1, example 2, example 3, example 4
    2. Energy stored in springs and dissipated in dampers: bungee jumper example

Week 5

  1. Force and velocity sources
    1. Practice with force and velocity sources
  2. Transformers: levers, work, and power
    1. Levers example 1, example 2, example 3

Week 6

  1. 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
    1. Example: counting state variables
    2. Example: finding state equations
  2. 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
    1. Example: complex numbers
    2. Example: superposition
    3. Example: damped natural vibration

Week 7

Electrical Systems

  1. Introduction: voltage and current, charge and current, voltage and potential, power source: batteries
  2. Resistors: constitutive law (Ohm's law), meter polarities, power, Kirchoff's laws
    1. Examples
  3. Capacitors: charge, capacitance, and energy
    1. Examples: resistors in series and parallel, capacitors in series and parallel

Week 8

  1. Formulating equations for circuits: circuit diagram notation, Kirchoff's laws, step 1 equations, step 2 state variables and equations
    1. Kirchoff's laws example 1, example 2
    2. Example: state variables and equations
  2. Simple RC circuits: RC time constant, charging up a capacitor (applet broken)
    1. Example: RC time constant
  3. Complex RC circuits
    1. Example 1, example 2, example 3

Week 9

  1. Inductors (applet broken)
  2. Circuits with inductors
    1. Example: simple circuit with an inductor
    2. Example: LC circuit and natural frequency

Week 10

Review and final quiz