Homework 5, due March 7, 2012

[goodwine]

Reading: All of chapter 7 except section 7.2.3.

Exercises: 7.2, 7.5, 7.8, 7.9.

[Jessie]

does a numerical computation package mean we can use the computer (such as matlab) to find the values?

[goodwine]

does a numerical computation package mean we can use the computer (such as matlab) to find the values?

Yes, matlab, a calculator, whatever you want to find the eigenvalues and eigenvectors.

[Jessie]

for problem 7.5 when you say to determine the eigen values if i=10 do you mean substitute i for the imaginary i?

[goodwine]

for problem 7.5 when you say to determine the eigen values if i=10 do you mean substitute i for the imaginary i?

No, sorry that's a typo. It is supposed to mean there are 10 masses.

[pat]

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?

[goodwine]

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?

No, it's all completely numerical using something like Euler's method or 4th order R-K.

[jmccormi]

No, it's all completely numerical using something like Euler's method or 4th order R-K.

Does this need to be done in Fortran or is Matlab ok?

[goodwine]

No, it's all completely numerical using something like Euler's method or 4th order R-K.

Does this need to be done in Fortran or is Matlab ok?

Either is ok as long as you can trust the answer.

[Jessie]

for problem 7.9 I don't understand what the f(t) is that you want us to plot.

[goodwine]

for problem 7.9 I don't understand what the f(t) is that you want us to plot.

It's the force, f(t), that's in the problem.

[Jessie]

for problem 7.9 I don't understand what the f(t) is that you want us to plot.

It's the force, f(t), that's in the problem.

i just realized that I was looking at problem 7.3 instead of example 7.3. Thanks

[jmagro]

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?

[astewar9]

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.

[goodwine]

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.

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.

[goodwine]

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?

I'll leave it to your judgement to determine the most effective way to communicate the nature of the response.