Homework 6, due October 13, 2010.

[goodwine]

Reading: I hope to get through Chapter 5 by the end of next week.

The first three problems constitute the re-take for the exam. It is not exactly the same, so don't work from the exam itself, but rather refer to this and the indicated problem in the course text. Submit this separately from the "regular" homework listed below.

1. 2.31, do all three parts from the book and also do part three as it was written on the exam.
2. Do problem 2 on the exam, but with one important difference: use F(t)=k_p(x_d - x(t)), which has the opposite sign of what was on the exam.
3. 3.29, do all 27 from the book, not just 13 like you had to do on the exam.

These three problems will be weighted as they were on the exam. Your score on these will be averaged with the exam to become your recorded examination score. You may work on these collaboratively, but what you submit must be in accordance with the course homework policy, which essentially does not allow copying and the work must reflect your own effort and understanding.

Exercises: from the course text, 5.3, 5.4 ad 5.7.

[cmork]

Problem 3.29 from the book asks us to sketch each of the plots by hand and then indicate which equation goes to which solution on that sketch. Can we answer in the same format as the test, only using words, or do you want us to draw the graphs as well?

[goodwine]

Problem 3.29 from the book asks us to sketch each of the plots by hand and then indicate which equation goes to which solution on that sketch. Can we answer in the same format as the test, only using words, or do you want us to draw the graphs as well?

Doing the same as the test is fine.

[sprender]

For 5.3, do we need initial conditions to solve this equation fully? Or do you want a general solution?

[goodwine]

For 5.3, do we need initial conditions to solve this equation fully? Or do you want a general solution?

I want the general solution. Write the series solution as a_0 times a series plus a_1 times another series. You should get that one of the series is sin and the other cos.

[sprender]

For problem 5.7, do you want us to solve Airy's equation as it is listed in that question with a (+) sign or as listed in the chapter with a (-) sign?

[goodwine]

For problem 5.7, do you want us to solve Airy's equation as it is listed in that question with a (+) sign or as listed in the chapter with a (-) sign?

I didn't really notice that I assigned a problem that I worked out twice in class. Since it's a + in the book I think I have to say to use that. A minus would just flip some signs anyway.

[ceramics]

Professor Goodwine, can you post the MATLAB and Fortran codes you created in class from Last Friday and today's classes?

[goodwine]

Professor Goodwine, can you post the MATLAB and Fortran codes you created in class from Last Friday and today's classes?

I already did. They are under "Course Administration"

[sprender]

When the questions ask for a series solution, do you want us to represent our answer as a partial sum or an equation containing the summation signs? I know we have to plot each as a partial sum, I am just unsure about the format of actual answer.

[goodwine]

When the questions ask for a series solution, do you want us to represent our answer as a partial sum or an equation containing the summation signs? I know we have to plot each as a partial sum, I am just unsure about the format of actual answer.

It's actually non-trivial to convert a recursion relation into an answer with a sum sign. So, the answer is \sum a_n t^n where a_0=something, a_1=something, etc, and then the recursion relation. As long as you have a way to compute each a_n, that's good enough.

[whawes]

For 5.4 are we supposed to use the method of numerical methods to find a solution that compares with the partial sums?

[goodwine]

For 5.4 are we supposed to use the method of numerical methods to find a solution that compares with the partial sums?

Yes.

[whawes]

Could you possibly post the matlab code for how to load the data.d/graph the columns?

[goodwine]

Could you possibly post the matlab code for how to load the data.d/graph the columns?

load data.d;
plot(data(:,1),data(:,2))

That's something you probably should have written down since I did it quite a few times in class.

[sprender]

What do we need to type into the terminal once we have established the .f file and how do we save the output into a readable file for Matlab to use?

[mhubbar3]

Professor Goodwine, I'm not sure if you remember, but the other day I was asking about problem 1 on the homework, specifically part 3 from the book (problem 2.31 in the book). I thought we had figured it out when you told me to convert the acceleration do to gravity from m/s^2 to km/hr^2, however, at the time, I forgot that this affects the value that you get for k from the equation for v_term (v_term = sqrt((m*g)/k), and using this new value for k when solving for the integration constant (c) in the equation for v(t), causes the solution for c to be non-real, because the term inside the arctanh operation is greater than zero...do you have any suggestions?

thanks

[goodwine]

Professor Goodwine, I'm not sure if you remember, but the other day I was asking about problem 1 on the homework, specifically part 3 from the book (problem 2.31 in the book). I thought we had figured it out when you told me to convert the acceleration do to gravity from m/s^2 to km/hr^2, however, at the time, I forgot that this affects the value that you get for k from the equation for v_term (v_term = sqrt((m*g)/k), and using this new value for k when solving for the integration constant (c) in the equation for v(t), causes the solution for c to be non-real, because the term inside the arctanh operation is greater than zero...do you have any suggestions?

thanks

If it's > 0 it should be ok. I'm pretty sure the range for tanh is (-1,+1).

[mhubbar3]

Sorry...I meant to say that it is greater than 1...my mistake

[mhubbar3]

If its easier, I can just talk to you about it before or after class tomorrow...and I really don't mean to drag this question on, I only persist because I, like most people I'm sure, did poorly on the test, and so want to understand whats going on in the problem and earn back as many points as possible

[goodwine]

Sorry...I meant to say that it is greater than 1...my mistake

I don't think I can be much help without seeing your work. The solution I've seen has a positive value and everything works out. That's fine. If you are satisfied with your effort, then drop it for tonight. I can talk about it for a bit after class tomorrow.