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ME 340 - Dynamics of Mechanical Systems

Course Information

Sections Time Location
AL3 & ZJ3 MWF 11:00 - 11:50 a.m. 4100 Sidney Lu Mechanical Engineering Bldg (LUMEB 4100)

Course Instructor:

Wenbin Wan


Office: LUMEB 3035

Office Hour: Mondays 2 p.m. - 3 p.m. or by appointment (calendly link sent in email)

Teaching Assistants:

Pranav Bhandari


Office Hour: Thursdays 6 p.m. - 8 p.m. @ LUMEB 0024

Guillermo Colin Navarro


Office Hour: Tuesdays 5 p.m. - 7 p.m. @ LUMEB 0022

Grader: Anisha Shukla (

More course info

Prerequisites: MATH 285 or MATH 286 or MATH 441; TAM 212; credit or concurrent registration in MATH 257 or MATH 415; credit or concurrent registration in ECE 205. Credit is not given for both ME 340 and either SE 320 or AE 353.

Textbook (optional): R. Esfandiari and B. Lu (2018) , Modeling and Analysis of Dynamic Systems, CRC Press.
ISBN-10:9781138726420 | ISBN-13:978-1138726420

Homework Assignments: There will be approximately 10 homeworks. You are encouraged to collaborate with others in the course, but you should hand in only your own work. No late homework will be accepted (however, your lowest homework score will be dropped). Dates will be clearly identified on Gradescope, where all assignments will be assigned, submitted, and graded. If the homework is LaTeX’d, it will get extra points.

Labs: The labs are managed by Dr. Daniel Block and Lab TAs. The information on lab sessions (lab handouts and other details) are at The labs are scheduled as follows.

[Updated on 8/18/2022] Please check the lastest Lab Schedule on the lab website.

Week of Lab
Sept 12 Lab #1
Sept 26 Lab #2
Oct 3 Lab #3
Oct 10 Lab #4
Oct 24 Lab #5
Nov 7 Lab #6
Nov 28 Lab #7

  • Lab attendance is compulsory and a passing grade for each of the seven laboratories is expected in this course.
  • You must complete the pre-lab assignment and become familiar with that week’s lab handout material before arriving to lab.
  • For all lab-related questions should be addressed to the lab TA assigned to your lab section.
  • Make use of the lab office hours.

Examinations: There will be in-class quizzes and midterm exams and a final exam of 2 hours. Formats/dates TBA.

  • Conflict Exams: Requests for a conflict or make-up examination will be individually evaluated. It requires a serious university approved documentation and are (almost) never granted. Please plan accordingly.

Extra Credit: You can earn an extra credit (EC) up to 5%. EC TBA.


Assessment Credit Comment
Homework assignments 45% Approximately 10 HWs
Labs 15% Compulsory
Quizzes 10% Time: TBA
Midterm 10% Time: TBA
Final Exam 20% Time: TBA
Extra Credit 5% TBA

Grading Scheme: The total percentage \(p\) correspnds to final grades as follows

  • A, if \(p \in\) [92%, 105%],
  • B, if \(p \in\) [80%, 92%),
  • C, if \(p \in\) [70%, 80%),
  • D, if \(p \in\) [60%, 70%), and
  • F, if \(p \in\) [0%, 60%).

Course Policy:

  • Please show respect for your classmates by limiting distractive behavior. You may use a smart phone, labtop or tablet to take notes or for other academic purposes directly related to the class. Mute your cell phones and other devices, and please keep any side discussions short and quiet.
  • You are expected to adhere to all of the rules pertaining to academic integrity outlined in the UIUC Student Code ( Failure to do so will result in an automatic F for the course and a recommendation for removal from the University.

Tentative Topics:

  • Mathematical Background
    • Complex numbers (review)
    • General differential equations
      • characterization, first-order form, phase portraits
      • numerical solutions,
      • first and second order ordinary differential equations
      • solution to linear time-invariant ordinary differential equations
      • matrix exponential, homogenous and particular solutions (review)
    • Laplace transforms (review)
    • First and second order ordinary differential equations
    • System Identification
  • Mechanical Modeling
    • Elements of physical systems
    • Free-body diagrams and Newton's second law
    • Lagrangian mechanics
    • Modal analysis
    • Equilibrium points
    • Linearization
    • Stability of dynamic systems
  • Input-Output Response
    • Free and forced response
    • Convolution
    • Transfer functions
    • Bode plots
    • Equivalent representations

Special Accommodations: If you have any condition, such as a physical or learning disability, which will make it difficult for you to carry out the work as it has been outlined or which will require special accommodations, please notify the instructor during the first week of the course with the appropriate written documentation. To contact the Division of Rehabilitation-Education Services (DRES), you may visit 1207 S. Oak St., Champaign, IL 61820, call (217) 333-1970, or email

RHF Resources: Emergencies can happen anywhere and at any time. It is important that we take a minute to prepare for a situation in which our safety or even our lives could depend on our ability to react quickly. When we’re faced with almost any kind of emergency – like severe weather or if someone is trying to hurt you – we have three options: Run, hide or fight.

  • Video
  • Handout

    Emergencies can happen anywhere and at any time, so it’s important that we take a minute to prepare for a situation in which our safety could depend on our ability to react quickly. Take a moment to learn the different ways to leave this building. If there’s ever a fire alarm or something like that, you’ll know how to get out and you’ll be able to help others get out. Next, figure out the best place to go in case of severe weather – we’ll need to go to a low-level in the middle of the building, away from windows. And finally, if there’s ever someone trying to hurt us, our best option is to run out of the building. If we cannot do that safely, we’ll want to hide somewhere we can’t be seen, and we’ll have to lock or barricade the door if possible and be as quiet as we can. We will not leave that safe area until we get an Illini-Alert confirming that it’s safe to do so. If we can’t run or hide, we’ll fight back with whatever we can get our hands on. If you want to better prepare yourself for any of these situations, visit Remember you can sign up for emergency text messages at


Dates Topics Materials* Comments
Week 1
(8/22 – 8/26)
Overview and syllabus reading
Complex analysis
Week 2
(8/29 – 9/2)
Complex analysis
Ordinary differential equations
HW 00 Due (9/3@10pm)
Week 3
(9/5– 9/9)
Ordinary differential equations [LecNote07]
No class on Mon. (Labor Day)
HW 01 Due (9/10 @10pm)
Week 4
(9/12 – 9/16)
State space representation
1st and 2nd order systems
F: In-class Quiz
Quiz 1(In-class on Fri.)
Week 5
(9/19- 9/23)
1st and 2nd order systems
Laplace transform
HW 02 Due (9/24 @10pm)
Week 6
(9/26 – 9/30)
Laplace transform
Inverse Laplace transform
Transfer function
HW 03 Due (10/1 @10pm)
Week 7
(10/3 – 10/7)
Transfer function [LecNote17]
HW 04 Due (10/8 @10pm)
Week 8
(10/10 – 10/14)
Transfer function
W: Midterm review
F: In-class Midterm
Midterm (In-class on Fri.)
Week 9
(10/17 – 10/21)
Transient response [LecNote21]
HW 05 Due (10/22 @10pm)
Week 10
(10/24 – 10/28)
Frequency response [LecNote24]
HW 06 Due (10/29 @10pm)
Week 11
(10/31 – 11/4)
Bode plots [LecNote27]
HW 07 Due (11/5 @10pm)
Week 12
(11/7 – 11/11)
Mechanical systems
Lagrangian dynamics
F: In-class Quiz
Quiz 2 (In-class on Fri.)
Week 13
(11/14 – 11/18)
Lagrangian dynamics
Equilibrium points and Linearization
HW 08 Due (11/19 @10pm)
Week 14
(11/21 – 11/25)
- - Fall Break
Week 15
(11/28 – 12/2)
Stability margins
HW 09 Due (12/2 @10pm)
Week 16
(12/5 – 12/9)
Special topic
W: Final review
12/7 (W): Last day of instruction
HW 10 Due (12/10 @10pm)
Final Week - - Final format/date TBA

Page maintained by Wenbin Wan