Homework 5, due March 7, 2012

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Homework 5, due March 7, 2012
Reading: All of chapter 7 except section 7.2.3.
Exercises: 7.2, 7.5, 7.8, 7.9.
Exercises: 7.2, 7.5, 7.8, 7.9.
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
does a numerical computation package mean we can use the computer (such as matlab) to find the values?

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Re: Homework 5, due March 7, 2012
Yes, matlab, a calculator, whatever you want to find the eigenvalues and eigenvectors.Jessie wrote:does a numerical computation package mean we can use the computer (such as matlab) to find the values?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
for problem 7.5 when you say to determine the eigen values if i=10 do you mean substitute i for the imaginary i?

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Re: Homework 5, due March 7, 2012
No, sorry that's a typo. It is supposed to mean there are 10 masses.Jessie wrote:for problem 7.5 when you say to determine the eigen values if i=10 do you mean substitute i for the imaginary i?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
For part 2 of problem 7.5, do we take our homogeneous solution from part 1 and add the particular solution, which is found by finding the magnification factors for each mass as in section 7.1.3?

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Re: Homework 5, due March 7, 2012
No, it's all completely numerical using something like Euler's method or 4th order RK.pat wrote:For part 2 of problem 7.5, do we take our homogeneous solution from part 1 and add the particular solution, which is found by finding the magnification factors for each mass as in section 7.1.3?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
Does this need to be done in Fortran or is Matlab ok?goodwine wrote:No, it's all completely numerical using something like Euler's method or 4th order RK.

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Re: Homework 5, due March 7, 2012
Either is ok as long as you can trust the answer.jmccormi wrote:Does this need to be done in Fortran or is Matlab ok?goodwine wrote:No, it's all completely numerical using something like Euler's method or 4th order RK.
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
for problem 7.9 I don't understand what the f(t) is that you want us to plot.

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Re: Homework 5, due March 7, 2012
It's the force, f(t), that's in the problem.Jessie wrote:for problem 7.9 I don't understand what the f(t) is that you want us to plot.
Bill Goodwine, 376 Fitzpatrick
Re: Homework 5, due March 7, 2012
i just realized that I was looking at problem 7.3 instead of example 7.3. Thanksgoodwine wrote:It's the force, f(t), that's in the problem.Jessie wrote:for problem 7.9 I don't understand what the f(t) is that you want us to plot.
Re: Homework 5, due March 7, 2012
Problem 7.5, Part 2.
What specifically should we plot? A plot of all ten masses' positions and velocities is unreadable. Do you want ten sub plots (one per mass) for each frequency, or all ten positions on one plot for each frequency? Would just plotting the motion of the first mass be okay for comparison?
What specifically should we plot? A plot of all ten masses' positions and velocities is unreadable. Do you want ten sub plots (one per mass) for each frequency, or all ten positions on one plot for each frequency? Would just plotting the motion of the first mass be okay for comparison?
Re: Homework 5, due March 7, 2012
For 7.9, how do we plot the force vs. time? I'm using ode45, and I can't plot the position of the mass, but I'm not sure how to plot the force.

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Re: Homework 5, due March 7, 2012
You have an equation for the force, so you should be able to plot it in one line. The point of the problem is to choose the force so that the mass behaves like you want, so you have to go back to the beginning of the problem to remember what it is you are actually doing.astewar9 wrote:For 7.9, how do we plot the force vs. time? I'm using ode45, and I can't plot the position of the mass, but I'm not sure how to plot the force.
Bill Goodwine, 376 Fitzpatrick

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Re: Homework 5, due March 7, 2012
I'll leave it to your judgement to determine the most effective way to communicate the nature of the response.jmagro wrote:Problem 7.5, Part 2.
What specifically should we plot? A plot of all ten masses' positions and velocities is unreadable. Do you want ten sub plots (one per mass) for each frequency, or all ten positions on one plot for each frequency? Would just plotting the motion of the first mass be okay for comparison?
Bill Goodwine, 376 Fitzpatrick