The behavior of physical systems is described by various fundamental laws of nature, such as Newton’s laws of motion, yielding mathematical equations whose solution approximates (or models) the actual behavior of the modeled system. In this class we analyze these mathematical models in hopes of describing the dynamical behavior of the physical system. This course concentrates on the analysis of linear models for the behavior of mechancial systems. We study the forced and transient response of single- and multi-degree-of-freedom systems.

Class Information

Grading

Office Hours

Office hours will be held in the respective offices unless noted at some later time (if, say, the offices become overcrowded I’ll try to find a new location). Office hours are an opportunity for you to get extra help, clarify a mistake, work problems, etc. However you must come prepared. Don’t walk in and ask us to teach you ``stuff’‘. Come with specific problems to be worked or specific ideas you don’t understand. If you can not make it to one of the scheduled office hours then feel free to drop by and if I have time I’ll be glad to help you, but be prepared to schedule a convenient time for us both.

Homework

Homework will be collected during class and (hopefully) returned the following week. Please work neatly, show all necessary steps (I don’t need to see that 2+2=4), and clearly denote your final answer. I view homework as the opportunity for you to learn the material covered in the lecture. As such, I feel that it is unrealistic for me to expect each of you to master the topics immediately (i.e., submitting a perfect homework). Therefore I feel that it is unfair for me to grade the homework as I would an exam, which is where you illustrate how much you have learned.

My resolution to this dilemma is to have the homework graded primarily on effort. Essentially, half of your grade comes from this alone, with the remaining half from your performance. Thus, realistically if you put forth a solid effort on the homework your grade will be relatively good. My balance in this leniency is provided by the weekly quizzes, which come directly from the homework and are graded as a exam.

Collaboration

You may work together on homework but any and all collaboration must be CLEARLY NOTED (this includes any sources used other than your text and own notes). In addition you must write up your own work.

Late Homework Policy

Late homework will be marked as follows:

Quizzes

Quizzes will be held weekly. Each will be composed of a single problem taken directly from the homework of the previous week. My goal is to motivate you to not only do the homework but to review the solutions once they are made available.

Exams and Final

There will be two exams during the semester. Each will be closed book but I will provide brief notes. Note: The final will be comprehensive.

Project

Outline

1. Introduction and Background
   [+]
   1. A Description of Harmonic Motion
   2. Spring-mass Model---An Overview
2. Newtonian Mechanics
   [+]
   1. Linear Momentum Balance
   2. Angular Momentum Balance
   3. Kinematics
3. Fundamentals of Mechanical Systems
   [+]
   1. Equilibrium Points
   2. Linearization
   3. Elasticity
      • Constitutive Modeling
      • Potential Energy
      • Structural Elements
   4. Dissipative Forces
   5. Equivalent Systems
4. Elements of Vibrating Systems
   [+]
   1. Elasticity/Springs
   2. Viscous Dampers
5. Free Vibrations of One-Degree-of-Freedom Systems
   [+]
   1. Modeling
   2. Undamped Systems
   3. Damped Systems
6. Harmonic Excitation of One-Degree-of-Freedom Systems
   [+]
   1. Harmonic Forcing
   2. Displacement Excitation
7. Multi-Degree-of-Freedom Systems

Ethics

1. Working together by solving problems is an effective way to learn. However, copying solutions from one another or out of the solutions manual is not acceptable and may constitute academic dishonesty. Copying solutions from one another or from the solutions manual may result in a one letter grade reduction for the course.
2. Any form of plagiarism is unacceptable and may result in disciplinary action.
3. All students are expected to behave in a respectful and appropriate manner in class. Students acting in a manner that is disruptive or impedes learning may be asked to leave the class. Students that are asked to leave will be required to meet with the instructor and may be referred to Student Judicial Affairs for review and possible disciplinary action.
4. The use of cell phones, pagers and other electronic devices is prohibited during class. Cell phones need to be placed into “silent / vibrate mode” during class or turned off. Laptops are permitted for the purpose of taking notes, software training and performing in-class assignments only and are not to be used for e-mail, instant messaging or other non-class activities.
5. Examinations are conducted as means to assess student learning and understanding of the course material. During examinations, students are expected to have no communication with others in or outside of class. Such communication or the copying of another student’s exam solutions will result in a grade of F for the examination and an F for the final course grade.