Homework assignments and
Mechanical Engineering 2030, Spring 2014, Dynamics
Please read the homework policy and homework grading policy.
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 23 assignment is not set in stone until Jan 24 at 3 AM).
Problems are from RP (Ruina and Pratap) unless otherwise specified or written out.
1/ 23 TH Introduction, review, assessment.
Note 1st HW due in ONE DAY. Second due in a week. Note Matlab for Dummies session on Sunday Jan 26.
* Read/Skim all of Ruina/Pratap Preface, Chapters 1-3 and Appendix A and Appendix C. Know what is there well enough that you can tell what you know and what you need to learn soon.
* Brush up on Matlab. For example, on the Rajesh page learn or refresh all that is in 'Matlab 101', the 2120 introduction and the Spring-Mass Oscillator.
A. Homework due FRIDAY JANUARY 24!
1) Problems 1a-d from the fall 2013 Statics Final
2) Challenge. Assume your are given the 3D coordinates for each of 4 points A,B,C and D (3X4=12 numbers total). Assume consistent units.
Write matlab commands to find the (minimum) distance between the lines defined by AB and CD. Test your code with some examples you understand.
This is not a simple problem. And it is not something you are expected to have memorized or memorize now. Rather it is a problem to push your conceptual understanding of vectors and the like. You will be much more in the spirit of the problem if you struggle with it and fail than if you look up how to do it, or have a friend tell you, and copy that down correctly.
3) Write: "I have read all of the course WWW pages and have these questions about the course policies __________".
B. Homework due FRIDAY JANUARY 31
1) 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 am registered for this course on blackboard." (Search for MAE2030.)
3) Write "I have registered my i-clicker."
4) Write "I can do all the preparatory problems for 9.1 except for ________."
5) 9.1.15 Very simple integration, based on a simple graph.
6) 9.1.16 Slightly harder integration, based on a graph.
7) 9.1.22 Grain falling though honey. Write an ODE and solve it. Easy.
8) Do the falling cone experiment: Make two cones, drop them simultaneously and see which falls fastest. Explain the result in a way that would convince you if it was written by another student who you did not already trust (and you had not already seen the experiment done).
1/28 TU 1-D Dynamics: F(x,v,t) = ma. The classic examples, springs,
dashpots, quadratic drag, gravity.
*Readings: Chapters 9.0, 9.1 and appendix C
*Rajesh Matlab tutorials
Homework due FRIDAY February 7
(As per the homework policy page, unless noted otherwise homewok associated with a given lecture is always due on the first Friday that at least 7 days after the lecture)
1) The exercise at the end of the Rajesh Spring-Mass System tutorials
1/30 TH More on ODE solutions, work, power and energy.
*Readings: Chapter 9.2
2) 9.1.26 Quadratic drag on a bullet. Gross (numerical solution, analytical solution is optional extra).
3) 9.2.3 This is easy, just vocabulary practice.
4) 9.2.10 The fall distance is the wall height + the leg bending. A simple problem.
5) 9.2.11 A simple energy problem using some wierd archery words.
6) 9.2.16 Constant power acceleration. This is a bit subtle and takes a bit of thought.
*Readings: 9.3 & 10.1: Vibrations: mass, spring and dashpot; Forcing and resonance
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).
2 ) 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.
3) 10.1.9 Basic damped oscillator problem. A numerical solution is perfectly fine. So is an analytic one. Your choice. Best to do both and compare.
*Readings: 9.4 & 9.5
4) 9.4.14 Two masses, three springs and a dashpot. Write and solve the equations.
5) 9.5.6 A simple problem taking you through the concepts and vocabulary of 1D collisions.
2/11 TU 1D collisions
1) 9.5.10 Tests if you can keep your hat on while calculating a sequence of collisions. And the answer is interesting.
2) 9.5.12 A bit of collision theory (the relation between e and energy dissipation)
2/13 TH Normal modes
3) 10.3.3 This is a very simple conceptual question, basically asking the definition of normal mode.
4) 10.3.8 A simple problem intended to make you think about motions of mulit-DOF systems
5) Write your own "midpoint" ODE solver analogous to this Euler solver. Practice by writing the code with any help and copying
and pasting as you like. After practice write this from start to stop without one glance at any sample,
only using Matlab errors and function help. Write on your HW: "I wrote this solver from start to stop without
looking at any samples or asking any humans for help." Test your code by checking your solutions to problem 4.
2/20 TH Particles in space
Readings: Chapter 11 (11.1-11.3)
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.
4) 11.2.19 A very simple problem to show if you know what the words mean.
5) 11.3.5 A computer simulation of a missile trajectory
2/25 TU Particles in space
Readings: 12.1 & 12.2
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
2/27 TH 1D constrained motion & pulleys
4) 13.1.6 Easy
5) 13.1.14b Slightly more involved pulley problem
6) 13.1.26 Pulley with spring, a bit more involved
***2/27 PRELIM 1, Olin 155/165 7:30 - 9:00PM +, covers through HW handed in 2/21***
(Note: You will be tested on Matlab. If you can write all code for HW above without copying, pasting or
looking at samples, you should be fine.)
3/04 TU Straight-line motion (Guest lecture: Kogin)
Readings: 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?
3/06 TH Straight-line motion, cont'd (Guest lecture: Kogin)
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.
3/11 TU Spring and Mass demonstration by Professor Wolfgang Sachse
HW: Due Monday March 24
Problems 1-4, from the in-class demo, in this zipped folder.
If you have questions about this assignment, ask them in email to Professor Sachse <email@example.com.
3/13 TH: Circular Motion
Readings: 14.1-2: Circular motion kinematics
Due Monday March 24
5) 14.1.1 Basically a vocabulary lesson/test
6) 14.1.15 A simple test of whether you can work with the ideas
7) 14.2.21 Everything (or most things) you should know about a simple pendulum
3/18 TU Dynamics of a particle in circular motion
1) 14.2.30 another circular motion problem, bead on a hoop with friction
2) 14.2.34 a classic energy/circular motion problem,
3/20 TH 15.1-4: 2D rigid-object rotation (mostly a review of freshman physics).
3) 15.1.8 computer graphics, using rotations to draw a rotated drawing.
4) 15.2.14 a simple problem. But you have to think to turn the words into sensible equations
5) 15.2.22 very simple gear problem
6) 15.2.24 A more challenging problem, with a math and computer flavor, about angular velocity. Could take an hour or so.
7) 15.4.10 quick easy mechanics problem
8) 15.4.20 easy mechanics problem (almost just kinematics)
*** 3/20 PRELIM 2, Olin 155/165 7:30 - 9:00PM+, Comprehensive, covers through HW handed in 3/14 ***
3/25 TU General motion of a rigid object
1) 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.
2 ) 16.1.1 Simple kinematics problem. Nothing hard.
3) 16.1.12 Javelin. Somewhat involved kinematics.
4) 16.2.7 Block in space with a force. Computer code and solution. Real work, but not hard.
5) 16.2.9 Suspended mass with cut springs. Simple instantaneous dynamics problem.
16.3-4: Kinematics and Dynamics 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.
4/10 TH Review (using tables from the back of the book) and 16.5: Collisions.
5) 16.5.8 Acrobat. Nothing too hard. But you have to keep your hat on through the various steps.
4/15 TU Collisions cont'd. 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.
4/17 TH 17.2 Rotating reference frames . 17.3 General expressions for
velocity and acceleration
4) 17.2.5 Very simple problem once you understand rotating coordinates.
5) 17.3.2 Bug walks on line on rotating turntable. Involved serious problem.
6) 17.3.11 Honeybee goes in circles on a rotating turntable. Not too hard.
4/22 TU 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.
*** 4/22 PRELIM 3, Olin 155/165 7:30 - 9:00PM+, Comprehensive, covers through HW handed in 4/18 ***
4/24 TH 18.1 Mechanics of a constrained particle, 18.2 1 DOF mechanisms.
4) 18.1.1(a-h): You should neglect gravity. Trivial. A pendulum in diguise, at least to start with.
5) 18.1.12 Bead on rotating stick. Not easy, not too hard.
6) 18.1.21 Bead in curved slot. Straightforward, some calculations.
7) 18.2.16 Which way does a bike accelerate? Needs very careful thought and set up
4/29 TU 18.3: 2 DOF mechanisms
Do the remaining problems, but do not hand them in.
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.
5/01 TH 18.3 cont'd
5) 18.3.10 Mass in slot. 2 DOF. Part f is a challenge.
6) 18.3.16 Pendulum on a cart. Easy problem.
5/06 TU 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.
*** 5/9 Friday: Homework exam (1PM - 5PM) and Makeup prelim (9 AM - 10:30+ AM), Thurston 2nd floor ***
Final Exam: Thu, May 15 7:00 PM Uris Hall G01