Homework and reading guide
TAM 203, Spring 2002

Homework guidelines: Homeworks are due at the start of tuesday lecture. You need not bring it to the front of the class, it will be collected from the class. On every homework assignment please do the things listed below. After a few weeks of getting used to these you will have to follow all of them to get any credit on homework.

a) On the top right corner neatly print the following, making appropriate substitutions as appropriate:
    Sally Rogers
     HW 2 Due Feb 5, 2002
    TAM 203
    Section 3 at 10:10
    TA: John Smith
STAPLE your homework in the top left corner.
c) At the top clearly acknowledge all help you got from TAs, Faculty, students, or ANY other source (but for lecture, text and section only). Examples could be "Mary Jones pointed out to me that I needed to draw the second FBD in problem 2." or "Nadia Chow showed me how to do problem 3 from start to finish." or "I basically copied this solution from a tau beta sigma frat file." etc. If your TA thinks you are taking too much from other sources he/she will tell you. In the mean time don't violate academic integrity rules and be unclear about what of your presentation you worked out on your own.
Every use of force, moment, momentum, or angular momentum balance must be associated with a clear correct free body diagram.
Your vector notation must be clear and correct.
All computer output should have your name clearly visible, as printed by the computer (e.g., title plots with your name, put your name in a comment in the first line of any .m files, etc.)
Every line of every calculation must me dimensionally correct. (Carry your units.)
Your work should be laid out neatly enough to read. Part of your job as an engineer is not just to get the right answer, but to communicate its justification clearly. So that is part of your job on the homework as well.
i) Some problems which are assigned may seem like make-work to you because you already know well how to do them.
If that is the case, you can answer a question and get full credit for it by writing "I can do this problem but don't feel
I will gain from writing out the solution". You can keep doing this unless your grader/TA challenges your judgement
about what you can do.

Homework 1, due Tuesday Jan 29 at the start of lecture: Solutions
Reading guide:(note, text homework problems are only available on WWW from text page)

Matlab book: You should know all the tutorials thoroughly. You should know the ODE section. You should skim the rest of the book so you know what is there, at least glance at every page.
Dynamics text part I:*First two tables inside the cover: Without studying them explicitly, you will learn all that's in these tables as the semester progresses. Read through them quickly at the start of the semester and check your progress occasionally as the semester progresses. *Preface: Read and absorb the "guide to student" and pseudo-code pages. *Chapter 1: Read and understand. *Chapter 2: You need to know all of this vector material well.

To hand in: Consider the two Matlab files below which we assume are both in the same directory on your computer.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%These 4 lines are in a script file               function zdot=iknowthis(t,z)
[t,z]=ODE23('iknowthis', [0 2*pi], [1 0]);        % These five lines are in the file iknowthis.m
plot(z(:,1),  z(:,2))                             z1 = z(1);  z2 = z(2);
axis('square')                                    z1dot=  z2;  z2dot= -z1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     zdot=[z1dot, z2dot]';

0) Please read the homework guidelines at the top of this WWW page.  Write "I have read and I understand the homework guidelines." 1) Answer this question without using a computer (give yourself at least half an hour to work on puzzling it out): What happens when you run the first file above? Explain your prediction. 2) Type the files in, and run the first. Print the results and hand them in. If what comes out is different than you expected, explain your error. 3) By changing the files above make a plot that shows an ODE solution that you think looks nice (visual aesthetics is the criterion). Title the plot with your name. Print out the files you used to that reflects the thought that went in to creating them. 4) 2.99 from text (vector review), download problem from text www page

Homework 2, due Tue Feb 5 at the start of lectureSolutions
Reading guide:
(All in Part I) Chapter 3: You need to know the material here well. Chapter 4: The ideas in the introduction and sections 4.1, 4.5 and 4.6 are essential for dynamics. Skim the rest of the chapter so you know what's there and can read it when you need it.
Problems: 1) 4.54    2) 4.61   3) 4.65   4) 4.67   5) 4.87
Homework 3, due Tue Feb 12 at the start of lecture. Solutions
Reading guide:
Chapter 5: sections 1-3. Read but don't fester over sections 4 and 5.
Problems: 1) 4.86. *) Make sure you can do problems 5.1-8, don't hand in. 2) 5.9 3) 5.14 4) 5.18 (use m = 1 kg, g=10 m/s^2, drag constant =C= 2 N/(m/s)^2) 5) 5.40
Homework 4, due Tue Feb 19 at the start of lecture. Solutions
Reading guide:
Chapter 5: sections 6-8. See the end of the preface for comments on "pseudo-code". See section 2.4, especially pages 58-59, about solving vector equations. 
Problems: 1)
5.28, 2) 5.59,  3) 5.64,  *) make sure you can do most of the problems in section 5.7.,  4) 5.120 (Typo: The symbols $'$ mean just '. That is [ 1 2 3]$'$ is supposed to be [1 2 3]'.),  5) 5.132
Homework 5, due Tue Feb 26 at the start of lecture. Solutions (corrected 3/7/02)
If you use the solutions in your homework, note that, like all other help, clearly on the homework you hand in.
Reading guide:
Chapter 5.9. Reading for Thursday lecture, not on prelim 1: section 5.10
Problems: 1) 5.141, 2) 5.142,  3) 5.143

Homework 6, due Tue March 4 at the start of lecture.  Solutions
Reading guide: 5.10, 6.1 (6.2 for thurs lecture but not homework)
Problems: 1) 5.147, 2) 6.2 3) 6.12 4) 6.14  5) 6.22, 6) 6.27

Homework 7, due Tue March 11 at the start of lecture.  Solutions
Reading guide: 6.1, 6.2 (7.1&7.2 for thurs lecture but not for homework)
Problems: 1) 6.28,   2) 6.35,   3) 6.43,   4) 6. 50,   5) 6.52,   6) 6.76.
Homework 8, due Thurs. March 27 at the start of lecture.  Solutions
Reading guide: 7.1-3 (7.4 for thurs lecture but not for homework)
Problems: 1) 7.1  2) 7.8 (text error, only one solution exists),   3) 7.14,   4) 7.41,   5) 7.47,   6) 7.59, 7) On the computer, draw a picture of anything. Then rotate it 120 degrees and draw it again on the same plot.
Homework 9, due Tues, April 2 at the start of lecture. Solutions
Reading guide: 7.4-6 (8.1 for thurs lecture but not for homework)
Problems: 1) 7.65,  2) 7.68,  3) 7.70,  4) 7.75,  5) 7.84,  6) 7.99
Homework 10, due Tues, April 9 at the start of lecture.  Solutions
Reading guide: 7.6, 8.1 (8.2 for thurs lecture but not for homework).
Review and master: pgs viii-ix, Chapters 1, 2.1 (especially sample 2.3), 2.4 (especially page 50), 3 (especially Fig. 3.4, box 3.1, and box 3.3), and appendix A (pgs 701-9).
Ramping up the standards: From this point on, to get any homework credit in all written work you need correct clear FBDs, correct clear vector notation and algebra, and correct clear use of units.
1) 7.134, 2) 7.143, 3) 7.141 (alpha = -15.4 rad/sec^2, T1 = 515 N, T2 = 364 N), 4) 7.149, 5) 8.1

Homework 11, due Tues, April 16 at the start of lecture.  Solutions
Reading guide: 8.2-8.4 (8.5 for thurs lecture but not for homework).
Problems: 1) 8.14,  2) 8.16,  3) 8.34,  4) 8.37,  5) 8.47, 6) 8.51

Homework 12, due Tues, April 23 at the start of lecture. Solutions
Reading guide: 8.5-9.1 (9.2 for thurs lecture but not for homework).
Problems: 1) 8.56 (take theta_double_dot=0,  2) 8.60,  3) 9.3,  4) 9.5,  5) 9.7, 6) 9.9a (solution in back of book is suspect.)
Homework 13, due Tues, April 30 at the start of lecture. Solutions
Reading guide: 9.2-9.5, 10.1.
Problems: 1) Find the radius of the osculating circle of a particle on the top of a rolling wheel in terms of the radius of the wheel. 2) 9.35 3) 9.41 4) 10.8 5) 10.24 6) 10.26
Homework 14, not handed in but due Tues, May 7. It is a real homework and is part of the final exam material. You will probably learn best by doing it with as little help as possible and not looking at the solutions until you are deeply stuck. Solutions.
Reading guide: 10.2-10.3
Problems: 1) 10.30, 2) 10.67, 3) 10.60, 4) 10.53, 5) 10.63

BONUS: Add up to an extra 5 points to your course score (Equiv of about 2 HW assignments). Estimated total time to complete is 2 hours (me) to 20 hours (someone who has to learn all as they go).
Due: May 19 midnight EST 100% strict. email submissions only. Credit only for complete good jobs: code runs and correct results are obtained. One hand in per person, but working together is allowed if fully acknowledged as per the homework directions at the top of this page.
Directions for handing in (a,b,c below are strict requirements, make sure you can handle them before the last minute, not following them will lead to lost files on my computer and no grade for you):
a) email a single file with the name   first_last_203extra.zip   (or .tar or .sit) where first_last is your name.
b) that file, when decompressed should contain only one folder named  first_last_203extra
c) that folder should have any number of matlab files inside, one of which drives all the others, and a file called *readme* that explains what you have done (word or pdf with appropriate figures, 72 dpi scan of hand work is ok as a single .pdf).
Assignment: (this, or make up a clear one on your own.) Make a matlab cartoon of a car, drawn as a rectangle looking down, as it skids to a stop with rear-wheel braking. One frame every fraction of a sec (you pick a time interval that looks nice) until the car stops. On this cartoon draw a curve of the path of the center of mass. Wheel base is 3m long, 2m wide. Center of mass in the middle of the car at ground level. Car is on level ground. Initial velocity is in the plus x direction at a speed of 30 m/sec. Initial angular velocity is zero. Initial angle is 1 degree counter clockwise. Assume a coefficient of friction of 1 on the skidding rear wheels (not me=zero as in lecture). Front wheels roll with no side slip. g = 10 m/s^2.
The basic problem setup is as in lecture of April 29. But you need to include the friction force on both of the skidding wheels. Also you need to use linear momentum balance to see how the speed changes. Finally you need to use kinematic relations to see how x and y components evolve, as well as theta. To see how to make movies see the Pratap text or the Fourier series example on the Matlab samples page. Your integrator might have trouble when the car comes to a stop after about 6 seconds, so you will have to take this into account somehow (two solutions: use "event detection" which is tricky the first time, or make your ODEfile give zero accelerations if all velocities are low enough).

Bonus project solutions: Here is a pretty good solutionfor the bonus project, by student Mike. One technical flaw is that Mike assumes that the effect of friction on the two skidding rear wheels is equivalent to a force on a single skid midway between the wheels. This is not right, but is probably a good approximation for most purposes.
PC version    Mac version