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Week 14 assignments: Collisions!

 

1) Read Chapter 11.6 and 11.7 in your classical mechanics text, for class on Monday 4/17/17. 11.7 will take us a while to finish, so probably need to reread it for Wednesday.

2) Homework #13 is due 04/26/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

  • 11.9, 11.19, 11.22 (make the plot in matlab), 12.2

3) make sure to turn any late homeworks in by 04/26/17 pm in Jiajie Xiao's mailbox in Olin 100.

Week 7 Assignments

1) Read Ch 6.1-6.3 in your classical mechanics text, for class on Monday 2/20/17

2) Read Chapter 6.4-6.4 in your Classical Mechanics text for class on Wednesday 02/22/17

3) Watch our video on path integrals and non-conservative forces for Monday 02/20/17.

3) Homework #7 is due 03/01/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

  • 6.6, 6.9, 6.10, and 6.11. 03/01/16 at 4pm.
  • For 6.9, make sure the final answer only has r's in it, not x,y, or z's

4) We now have a departmental webpage with links to suggested math videos for review. If you haven't, I encourage you to review the one line integrals for Monday 2/20/17.

Week 6 assignments

1) Read Ch 5.1-5.4 in your classical mechanics text, and review The Mathematics Companion section 2.3 on Vector Analysis for class on Monday 2/13/17

2) Read Chapter 5.5-5.6 in your Classical Mechanics text and review The Mathematics Companion sections 2.4 and 2.5 on partial derivatives and multiple integrats for class on Wednesday 02/15/17

3) Watch our videos on solving the critically damped harmonic oscillator and Springs in parallel and series by Monday 02/13/17, and on the curl of a gradient by Wednesday 02/15/17.

3) Homework #6 is due 2/22/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

A) Problems 4.13, 4.14, 5.3, 5.6 and 5.13 from your classical mechanics textbook

  • Note that the M matrix in 14a has a typo. Figure out what the typo is.
  • You are welcome to solve 14b computationally, but not the rest of the assignment.
  • Do 5.6b, and 5.13 using the levi-civita symbol, aka anti-symmetric tensor aka alternating tensor. Any other solutions will be counted wrong.

B) The computational problem assigned in class on 02/17/17.

4) We now have a departmental webpage with links to suggested math videos for review. I encourage you to review the ones on Cross products, Line integrals and Eigenvalues and Eigenvectors.

Week 5 Assignments

1) Read Chapter 4.1-4.6 in your Classical Mechanics text for class on Monday 2/06/17

2) Read Chapter 4.1-4.12 in your Classical Mechanics text for class on Wednesday 02/08/17

3) Watch our videos on the Hanging Spring-Mass system and Springs in parallel and series by Wednesday 02/08/17.

3) Homework #5 is due 2/15/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

A) Problems 4.4, 4.5, 4.9, and 4.11 from your classical mechanics text.

B) The computational problem assigned in class on 02/10/17.

Note: The problems from your textbook need to be solved by hand. Using symbolic math solvers is not allowed.

Week 4 assignments

 

1) Read Chapter 3.1-3.4 in your Classical Mechanics text for class on Monday 01/30/17

2) Read Chapter 3.5 in your Classical Mechanics text for class on Wednesday 02/01/17

3) Read or re-read Chapter 2.1.1-2.1.17 and re-read Chapter 1.9.4 from The Mathematics Companion.

4) Homework #4 is due 2/08/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

A) Problems 3.9, 3.10, 3.11, 3.12, and 3.13 from your classical mechanics text.

B) The computational problem assigned in class on 02/03/17, which will involve damped, and driven oscillators.

Note: Problems 3.9-3.13 need to be solved by hand. Using symbolic math solvers is not allowed.

 

Week 3 Assignments

Later than I had planned to post,

1) Read Chapter 3.1-3.4 in your Classical Mechanics text for class on Wednesday 01/25/17

2) Watch and work through our video on quadratic drag.

3) Watch and work through our video on the Matlab Publish command.

4) Homework #3 is due 2/01/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

A) Problems 2.15, 2.17a (no computation), 3.2 and 3.3 (use matlab for your plot) from your text

B) Using the leapfrog integrator, model throwing a ball straight up in the air with linear drag. Find the position as a function of time, and the time it takes the ball to come back to the origin. You may set the mass as 1kg, and the origin at 0, but examine what happens with a variety of initial conditions and drag coefficients. Do at least four cases: two initial velocities that vary by at least an order of magnitude with at least two different drag coefficients that vary by at least an order of magnitude. Discuss what happens as the drag changes and the initial velocity changes.  Make sure to increase the number of time-steps so the time it takes for the ball to come back to x=0 converges to 1% or better.

C) Show that Euler's formula (e^(ix)=cos(x)+isin(x)) works by expanding both sides to fifth order in x and collecting terms. (It will still work if you collect all terms, but this isn't a math class.)

Note: With the exception of the computational problem and the plotting in 3.3, the problems need to be solved by hand. Using symbolic math solvers is not allowed.

5) You may want to watch our solution to problem 2.5.

6) Read or re-read Chapter 2.1.1-2.1.7 from The Mathematics Companion, for this week and for Monday. This has far more detail than we will explicitly use in class, but contains the theory behind what we will do.

 

Week 2 Assignments

1) Read Chapter 2 in your Classical Mechanics text for class on Wednesday.

2) Review material in the Mathematics Companion. This week, we will use material from 1.5, 1.6, 1.7, and 1.9.

3) Watch and work through in matlab our video on Leapfrog integration.

4) Homework #2 is due 1/25/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:

A) Problems 1.8, 1.9, 2.5, 2.6, 2.8 from your text

  •  2.8 should be considerably more difficult than the other problems.
  • Hint: this integral table might be of use.

B) Using the leapfrog and Euler-Cromers integrators, redo the computational problems from HW #1 and comment on the differences between Euler, Euler-Cromers and Leapfrog in terms of the steps needed.

 

  

 

Homework #1

The first homework for the course. 

A few points:

1) plots have labels and titles.

2) don't pick an initial condition that results in no motion.

3) When asked to comment on what changes, discuss how the modeling of the motion varies with timestep for the two different cases including comparing the time steps needed for different force laws and the specified accuracy.

Here are the expectations for writing up homework assignments.

Week 1 Announcements and assignments

This week, Jan 11 and 13th, we will focus on reviewing Newton's equations and introducing Matlab as a tool for solving problems in classical mechanics.

Your assignments:

1) Read Chapter 1 in your Classical Mechanics text. Ideally in time for class on Wednesday but absolutely in time for class on Friday.

2) Install Matlab on your laptop and make sure it runs. You can obtain it at software.wfu.edu . If you have difficulty installing Matlab, go to the Bridge. Make sure you have an working copy by class on Friday.

3) Review material in the Mathematics Companion. In particular, we will use material from 1.1, 1.3, 1.4 this week, along with 2.1.1. However, next week, we will use material from 1.5, 1.6, 1.7, and 1.9, so I encourage you to review ahead.

4) Watch, and work along with in Matlab, our introductory video on Matlab before class on Friday. 

5) Watch our video on Leapfrog integration. We might not get to until next week, and it might be a little challenging, but go ahead and watch it now first before class on Friday.

Our first homework will not be due until the 18th.