Engineering Analysis 3

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EA3 System Dynamics, Spring Quarter 2024

This wiki page:, or just google "NU EA3" or "Northwestern EA3" and it will come up near the top.

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. You may go to a discussion section you are not registered for if there is room in the room.

  • Section 20: Lecture 10-10:50 MWF Annenberg G15; TA-led discussion Tuesday, Frances Searle 1441
    • Instructor: Prof. Kevin Lynch,
    • TAs: Ayesha Ahmed,, and Chyim Bowen, (also Megan Black,
  • Section 21: Lecture 11-11:50 MWF Pancoe Auditorium; TA-led discussion Tuesday, Pancoe Auditorium
    • Instructor: Prof. Jeremy Keys,
    • TAs: Xiaoyu Xie,, and Gaurav Tyagi,
  • Section 22: Lecture 1-1:50 MWF, Pancoe Auditorium; TA-led discussion Tuesday, Tech M345
    • Instructor: Prof. Jeremy Keys,
    • TAs: Ruoming Gong,, and Plenyo Gonzaga Araujo,
  • Section 23: Lecture 2-2:50 MWF, Tech M345; TA-led discussion Tuesday, Pancoe Auditorium
    • Instructor: Prof. Manohar Kulkarni,
    • TAs: Nandeesh Bhatia,, and Tapiwanashe Bhibho,





Office Hours

Office hour schedule, beginning April 1. 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 9-11 pm
Mon (none Memorial Day) x x x x x x Ahmed Ahmed Xie
Tues Keys Bhibho Bhibho Bhibho
Wed Araujo Araujo Araujo Lynch Gong Gong Kulkarni, Tech B290 Gong Tyagi (by zoom; link in Canvas)
Thurs Keys Bowen Bowen Bowen Ahmed x x x
Fri x x Bhatia Bhatia Bhatia

Office hours are subject to change. Please check the schedule before going to office hours to get the latest information.

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 other sources, nor are you allowed to share your answers or code with others. If you use generative AI to help you with your work, you are obligated to cite the source and nature of the help; for example, if you turn in code generated in whole or in part by generative AI, you must cite the AI software in the comments, and you are required to understand how and why the code works. (Note also that electronics are not available during tests, so submitting code you do not understand will not help you prepare for tests.) 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.

Religious Holidays

Provost's statement on accommodations for religious holidays.

Course Schedule and Quizzes

Lectures MWF by the instructors. Tuesday discussion sessions led by the TAs, primarily focused on solving problems. First day of class is Tuesday March 26, but following a Monday schedule. We begin the normal rhythm Wednesday March 27. Office hours begin Monday April 1, and the first homework is due Thursday April 4.

Lectures will be recorded and available on Canvas via Panopto if you miss a class.

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

  • Monday April 22
  • Monday May 13
  • Friday May 31 (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, make sure to let your instructor know, and report to the following room 30 minutes before your normal class time on days of quizzes. This will be a low-distraction environment.

  • Monday April 22: Tech L440
  • Monday May 13: Tech L440
  • Friday May 31: Tech E311

Because of the large size of the course, make-up quizzes are not offered. If you need an accommodation for an emergency, you will be directed to the undergraduate engineering office to make the request. If you have a scheduled, unavoidable, legitimate conflict, it is your responsibility to report it to your instructor at the beginning of the quarter.


Homeworks are due each Thursday (except the first and last week) at 5 PM, and homework solutions will be released Thursday nights. Homeworks must be submitted electronically through Canvas. Late submissions 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 to accommodate an emergency, celebration of a religious holiday, homeworks that are just a few minutes late, homeworks that you completed on time but forgot to submit, or any other circumstance.

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. When including code in the pdf, make sure to print the code as pdf (don't take images of code, for example) so the code is copy-and-pastable.


The three quizzes count for 75% of your class grade. Homeworks account for the remaining 25%. 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.

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

Monday Quiz

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

Week 8

Monday Quiz

  1. Formulating equations for circuits: circuit diagram notation, Kirchhoff's laws, step 1 equations, step 2 state variables and equations
    1. Kirchhoff'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 Friday Quiz