TAM 2030, Spring 2013

Study advice: Try to do assigned homework problems from beginning to end with no help from book, notes, solutions, people, etc., yourself without looking up even one small thing. Explain, at least outloud to yourself, every step. If you did need help, then afterwards start the problem over by yourself without looking up even one small thing. Then similarly do other problems that are like the assigned problems. Then do old prelims and exams. Finally, for A+ style studying, invent and solve your own problems.

Homework assignments below subject to change until
3 AM of the morning after the lecture associated with the HW
(e.g., Jan 22 assignment is not set in stone until Jan 23 at 3 AM).

Problems are from RP (Ruina and Pratap) unless otherwise specified or written out.

### Lecture dates:

Jan 22 Tu: HW 0 due Jan 29. Course introduction.. Section 9.1: Force and motion in 1D. Falling balls (Galileo), falling cones.
1) Read the Policies above and on the linked pages above. Write "I have read and understood the HW and academic integrity policies for this course. The questions I have about them are: ____." Fill in the blank. Print and sign your name. Note! Academic integrity hearings are _NOT_ FUN!
2) Write "I have registered for this course on blackboard." (Search for ENGRD2030.)
3) Write "I have registered my i-clicker."
Write: "I have read _____% of the preface, Chapter 1 and Section 9.1."
5) Write "I can do all the preparatory problems for 9.1 except for ________."
6) 9.1.15 Very simple integration, based on a simple graph.
7) 9.1.16 Slightly harder integration, based on a graph.
8) 9.1.22 Grain falling though honey. Write an ODE and solve it. Easy.
9) Explain the falling cone experiment as best you can.

Jan 24 Th HW 1 due Feb 5, Force and motion in 1D cont'd.
1) 9.1.26 Quadratic drag on a bullet. Gross (numerical solution, analytical solution is optional extra).

Jan 29 Tu
HW 2 due Feb 5, Section 9.1 cont'd: Numerical Solution of ODEs. Demo of harmonic oscillator.
1) 9.2.3 This is easy, just vocabulary practice.
2) 9.2.10 The fall distance is the wall height + the leg bending. A simple problem.
3) 9.2.11 A simple energy problem using some wierd archery words.
4) 9.2.16 Constant power acceleration. This is a bit subtle and takes a bit of thought.

Jan 31 Th HW 3 due Feb 12, 9.2, Energy methods in 1D
0) Don't hand in: Redo 9.1.26 without looking up anything.
1) 9.3.6, because of gravity the concept of "rest position" for a hanging mass has two possible meanings. This problem takes you slowly through the issues associated with defining displacement various ways. The last part takes some thought (of course you should give a justified answer, not a guess).

Feb 5 Tu
HW 4 due Feb 12, 9.3 & 9.6: Vibrations: mass, spring and dashpot; Forcing and resonance.
Matlab .
1) 9.3.8 Part c requires careful thought because the period of time of contact with the trampoline is not half the period of the associated harmonic oscillator (because of gravity, the feet don't leave the trampoline at the mid-point of the oscillations). Doing this problem well is not quick.

Feb 7 Th HW 5 due Feb 19, 9.4, 10.1, 9.5: Coupled motions and collisions in 1D
1) 9.4.14 Two masses, three springs and a dashpot. Write and solve the equations.
2) 9.5.6 A simple problem taking you through the concepts and vocabulary of 1D collisions.
3) 9.5.10 Tests if you can keep your hat on while calculating a sequence of collisions. And the answer is interesting.
4) 9.5.12 A bit of collision theory (the relation between e and energy dissipation)

Feb 12 Tu HW 6 due Feb 19,  10.3: Normal modes (lots of demos on Feb 14 lecture. Also matlab for modes and collisions)
1) 10.3.3 This is a very simple conceptual question, basically asking the definition of normal mode.
2) 10.3.8 A simple problem intended to make you think about motions of mulit-DOF systems.

Feb 14 Th HW 7 due Feb 26, 11.1: A particle in space, momentum & energy, celestial mechanic.
1) 11.1.22 In spirit this is extremely close to a 3D particle statics problem.
2) 11.1.26 Add part d) What is the general motion (what is the full set of trajectory shapes that is possible)? This problem is genuinely interesting. It has all the look of an intractable non-linear problem but turns out to be a simple linear problem.
3) 11.1.31 This problem should expand your understanding of parabolic-flight ballistics to the more realistic ballistics of things where air drag is important.

Feb 19 Tu
HW 8 due Feb 26, 11.2-3: Coupled particle motion, particle collisions
1) 11.2.19 A very simple problem to show if you know what the words mean.
2) 11.3.5 A computer simulation of a missile trajectory

Feb 21 Th HW 9 due Mar 5, 12.1-2: Particles in space
1) 12.1.10 A cute simulation of 3 balls in space.
2) 12.2.7 Very much like lecture example (2 balls colliding in 2D)
3) 12.2.10 Note that 12.2.7 is not of the standard form, so you can use this program to check your answer to 12.2.7, but not to generate it

Feb 26 Tu
HW 10 due Mar 5, 13.1: 1D constrained motion & pulleys
1) Write "I have read through Chapter 2 of the text. The material there that I have to study more is (fill in as appropriate)."
2) 13.1.6 Easy
3) 13.1.14b Slightly more involved pulley problem
4) 13.1.26 Pulley with spring, a bit more involved

Feb 26 Prelim 1, Covers through through HW handed in Feb 26, lab 1, lectures and readings (+ prereq courses). 7:30 PM - 9:00 + PM, Uris G-01

** NEWS FLASH. The actual lectures are a full lecture behind this schedule. But the homework is sticking on schedule. As part of catchup, learn the kinematics of pulleys in the book Chapter 13.1 and look at the videos from 2011: Lecture 11 (the last 14 minutes) and Lecture 12 (the first 25 minutes).

Feb 28 03 Th HW 11 due Mar 12, 13.2 1D motion with 2D & 3D forces
1) 13.2.11 Simple constrained-object problem
2) 13.2.14 Il-posed constrained-object problem, why?
3) 13.2.25 Car braking. Long statement, but basically just a sequene of hints for a problem that could be stated briefly.
Worth doing carefully and well.
4) 13.2.43 3D supported plate, good place to practice 3D vectors. Not hard once you know how.
5) 13.2.47 3D braked car. You have to know your 3D vectors for such problems.

Mar 05 Tu HW 12 due Mar 12, 14.1-2: Circular motion kinematics
1) 14.1.1 Basically a vocabulary lesson/test
2) 14.1.15 A simple test of whether you can work with the ideas
3) 14.2.21 Everything (or most things) you should know about a simple pendulum

Mar 7 Th HW 13 due THURSDAY MARCH 28, 14.2: Dynamics of a particle in circular motion (Guest lecture)
1) 14.2.30 another circular motion problem, bead on a hoop with friction
2) 14.2.34 a classic energy/circular motion problem,

Mar 12 Tu HW 14 due THRUSDAY MARCH 28, 15.1-2: 2D rigid-object rotation.
1) 15.1.8 computer graphics, using rotations to draw a rotated drawing.
2) 15.2.14 a simple problem. But you have to think to turn the words into sensible equations
3) 15.2.22 very simple gear problem
4) 15.2.24 A more challenging problem, with a math and computer flavor, about angular velocity. Could take an hour or so.

Mar 14 Th HW 15 due April 2,  15.2: 2D rigid-object angular velocity.
15.3: Polar moment of inertia. Read, but no assigned problems
15.4: Dynamics of rigid-object planar circular motion.
1) 15.4.10 quick easy mechanics problem
2) 15.4.20 easy mechanics problem (almost just kinematics)
3) 15.4.34 multipart pendulum problem. For parts (a,b) answer in terms of sensible variables. A computer will help with some of the plots. This problem will take at least a good hour to do well.

**** Spring Break *****

Mar 26 Tu HW 16 due Apr 2, 16.1: Rigid-object kinematics
1) 16.1.1 Simple kinematics problem. Nothing hard.
2) 16.1.12 Javelin. Somewhat involved kinematics.

****Mar 26 PRELIM 2, INCLUSIVE (from the start of the semester, including pre-requisite courses), covers through HW handed in on MARCH 12. Covers Lecture lecture through Tuesday March 12. Covers Text through chapter 14. Uris G-01

Mar 28 Th HW 17 due Apr 9, 16.2 Dynamics of a rigid object
1) 16.2.7 Block in space with a force. Computer code and solution. Real work, but not hard.
2) 16.2.9 Suspended mass with cut springs. Simple instantaneous dynamics problem.

Apr 02 Tu
HW 18 due Apr 9, 16.4: Dynamics of rolling and sliding
16.3 Kinematics of rolling and sliding
1) 16.3.3 Plotting things about the motion of a point on a rolling tire. Probably needs a nice computer plot.
2) 16.4.6 Spool is pulled by a rope. A real problem, but not super hard.
3) 16.4.9 Napkin ring. This problem requires careful setup and real thought.
4) 16.4.23 Disk in cylinder. A real problem. Takes time and care.

Apr 04 Th
HW 19 due Apr 18, 16.4 cont'd
16.5: Collisions.
1) 16.5.8 Acrobat. Nothing too hard. But you have to keep your hat on through the various steps.

Apr 09 Tu
HW 20 due Apr 18, 17.1: Polar coordinates & path coordinates
1) 17.1.5 Simple polar coordinates problem, at least once you understand polar coordinates.
2) 17.1.6 Like 17.5, but concerning acceleration. May take some thought. But not hard once you get it.
3) 17.1.10 Very simple vocabulary test, but with a neat drawing.

Apr 11 Th
HW 21 due Apr 23, 17.1 cont'd
17.2 Rotating reference frames
1) 17.2.5 Very simple problem once you understand rotating coordinates.
17.3 General expressions for velocity and acceleration
2) 17.3.2 Bug walks on line on rotating turntable. Involved serious problem.
3) 17.3.11 Honeybee goes in circles on a rotating turntable. Not too hard.

Apr 16 Tu
HW 22 due Apr 23, 17.4: Kinematics of 2D mechanisms
1) 17.4.1 Slider crank. Involved kinematics problem. Have to keep your hat on.
2) 17.4.4 Interacting rods. Hint: vel of C = vel of C.
3) 17.4.10 Interacting rods, considering acceleration. Not easy, not hard.

April 16 Prelim 3, Inclusive, covers through HW handed in April 9 and the actual lecture of April 4. 7:30 PM - 9:00 + PM, Philips 101 & 203.

Apr 18 Th HW 23 due April 30, 17.4 cont'd
18.1 Mechanics of a constrained particle
1) 18.1.1(a-h): You should neglect gravity. Trivial. A pendulum in diguise, at least to start with.
2) 18.1.12 Bead on rotating stick. Not easy, not too hard.
3) 18.1.21 Bead in curved slot. Straightforward, some calculations.

Apr 23 Tu
HW 24 due April 30,18.2: 1 DOF mechanisms.
1) 18.2.16 Which way does a bike accelerate? Needs very careful thought and set up.

Apr 25 Th HW 25 due May 7, 18.3: 2 DOF mechanisms
1) 18.3.1 Particle on a springy leash.  Test of concepts. Not hard.
2) 18.3.3 The same problem as above, in disguise.
3) 18.3.8 Yo yo.  Pretty easy too.
4) 18.3.10 Mass in slot. 2 DOF. Part f is a challenge.

April 30 Tu HW 26 due May 7, 18.3 cont'd
Do the remaining problems, but do not hand them in.
1) 18.3.16 Pendulum on a cart. Easy problem.

May 02 Th HW 27 due May 7, 18.3 cont'd
1) 18.3.28 Double pendulum. A special relatively easy case of a hard problem.
2) 18.3.30 Rimless wheel. Long involved problem.

May 7:  All extra credit projects are due.

May 4 Sat:
Homework exam (1PM - 5PM) and Makeup prelim (9 AM - 10:30+ PM), Thurston 2nd floor

Final Exam: Fri, May 10, 2013, 2:00 PM - 4:30 PM