Homework 3, due February 4, 2008.

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Homework 3, due February 4, 2008.
From the course text: 6.1 (if you have not already done it), 6.96.12, 7.4 and 7.5. If you did do 6.1 on homework 2, you don't have to do it again, but indicate that you did so that it is easy for the graders to keep track of it.
Bill Goodwine, 376 Fitzpatrick
Re: Homework 3, due February 4, 2008.
Problem 6.8 was assigned last week. Should we still work through it?

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Re: Homework 3, due February 4, 2008.
Sorry, that was a mistake. I edited the assignment to remove it.sjensen1 wrote:Problem 6.8 was assigned last week. Should we still work through it?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 3, due February 4, 2008.
Professor,
If we did problem 6.1 in assignment #2, but applied the incorrect method to solve for the solution may we redo it to obtain full credit as opposed to the credit that might have been lost by doing it in assignment #2?
If we did problem 6.1 in assignment #2, but applied the incorrect method to solve for the solution may we redo it to obtain full credit as opposed to the credit that might have been lost by doing it in assignment #2?
Re: Homework 3, due February 4, 2008.
Should we assume any kind of units for problem 7.4 or should we leave b, k, and m as variables?
Re: Homework 3, due February 4, 2008.
Both questions are about 6.11:
1) For irrational numbers (1+/ sqrt(15)), two of the eigenvalues of the matrix, is there a relationship between their eigenvectors, like there is with complex numbers?
2) Evaluating (Alamda*I) where lamda is 1+/ sqrt(15), I got eigenvectors of [0;0;0;0] for both. I checked my math for both, and it seems right. Are two trivial eigenvectors acceptable, since the other eigenvalues yield nontrivial eigenvectors?
1) For irrational numbers (1+/ sqrt(15)), two of the eigenvalues of the matrix, is there a relationship between their eigenvectors, like there is with complex numbers?
2) Evaluating (Alamda*I) where lamda is 1+/ sqrt(15), I got eigenvectors of [0;0;0;0] for both. I checked my math for both, and it seems right. Are two trivial eigenvectors acceptable, since the other eigenvalues yield nontrivial eigenvectors?
Re: Homework 3, due February 4, 2008.
I'm actually wondering myself if, when it says, "Determine the equations of motion," it means to just find the differential equations?wgarraha wrote:Should we assume any kind of units for problem 7.4 or should we leave b, k, and m as variables?

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Re: Homework 3, due February 4, 2008.
Yes the equations of motion are the differential equations. Unless it says to solve them, you don't have to do so.satkinso wrote:I'm actually wondering myself if, when it says, "Determine the equations of motion," it means to just find the differential equations?wgarraha wrote:Should we assume any kind of units for problem 7.4 or should we leave b, k, and m as variables?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 3, due February 4, 2008.
for problem 7.5 when it says to write a computer program to determine an approximate numerical solution for the system, do you mean you want us to show a graph of the motion vs. time, and if so, do we need to show each mass or just the first one, or is it asking for something else?

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Re: Homework 3, due February 4, 2008.
It's intentionally openended. Submit something that clearly communicates the nature of how the masses are moving. It's up to you to determine what you think is best.gtorrisi wrote:for problem 7.5 when it says to write a computer program to determine an approximate numerical solution for the system, do you mean you want us to show a graph of the motion vs. time, and if so, do we need to show each mass or just the first one, or is it asking for something else?
Bill Goodwine, 376 Fitzpatrick

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Re: Homework 3, due February 4, 2008.
You can redo it, but put a note on your homework saying that you want this one to count and not the previous one.Anon wrote:If we did problem 6.1 in assignment #2, but applied the incorrect method to solve for the solution may we redo it to obtain full credit as opposed to the credit that might have been lost by doing it in assignment #2?
Bill Goodwine, 376 Fitzpatrick

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Re: Homework 3, due February 4, 2008.
For the first question, it is an extra term since it does not depend on any of the components of xi.I had a few questions on problem 7.5: How do you fit the f(t)
equation into the xsidot = a*xsi? Is it just an added on thing after
that? Secondly, in the computer program is it possible to input
everything as an array or do you need to do x1dot(1) = x1(2),
x1dot(2) = etc..? Thanks
For the second question, it depends on the programming language you use, but the answer is probably that you have to input everything term by term.
Bill Goodwine, 376 Fitzpatrick

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Re: Homework 3, due February 4, 2008.
Either you are computing the powers incorrectly or after the powers you can do a lot of row reduction. I don't remember exactly for the assigned questions, but you are not guaranteed a matrix full of zeros. You may have to do some row reduction to get m rows of zeros.I am having trouble solving the differential equations with repeated eigenvalues. In the text book, in both examples the matrix (AxI)=0 (where x = lambda), when squared or cubed or multiplied to the fourth power, always becomes a matrix of zeros. But in the homework problems, the matrices do not( they oftentimes just become greater ratios of the same number), and I can never find more than one eigenvector, or sometimes even no eigenvectors. In any case, I believe that I need m eigenvectors before I can plug them back into the given equation. Is there something that I am doing wrong?
Bill Goodwine, 376 Fitzpatrick