Homework 2, due Jaunary 28, 2009.

Due Wednesday, January 28, 2008.
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goodwine
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Homework 2, due Jaunary 28, 2009.

Post by goodwine »

Submit your homework with your ND student ID number on it.

Reading: Chapter 6, Appendix B and section 7.3.

Exercises: 6.1, 6.5-6.8, 7.1-7.3.

In addition, for problems 7.1 and 7.2, let all the masses, spring constants and viscous damper constants be equal to 1 and determine the general solution for the system. You may use matlab or other numerical computation package to compute the eigenvalues and eigenvectors. Assume the masses start from rest and
  • for 7.1, let the initial positions of the two masses be x1=1 and x2=-0.5, and plot the motion of the two masses versus time on the same plot; and,
  • for 7.2, let the initial positions of the three masses be x1=0, x2=1, x3=-1 and plot the motion of the three masses versus time on the same plot.
Bill Goodwine, 376 Fitzpatrick
imills

Re: Homework 2, due Jaunary 28, 2009.

Post by imills »

Professor,

I think for problem 7.3, part 2, the eigenvectors are n long (not 2n long), and A exists in the n*n real (not the 2n*2n real).

-IM
goodwine
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Re: Homework 2, due Jaunary 28, 2009.

Post by goodwine »

imills wrote:Professor,

I think for problem 7.3, part 2, the eigenvectors are n long (not 2n long), and A exists in the n*n real (not the 2n*2n real).
No, it's 2n. n of those are for the positions of the masses and the other n are for the velocities.
Bill Goodwine, 376 Fitzpatrick
msobole1

Re: Homework 2, due Jaunary 28, 2009.

Post by msobole1 »

Professor,

Should the last spring be labeled k_n and the last damper be b_n, as opposed to what is written in the book?
goodwine
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Re: Homework 2, due Jaunary 28, 2009.

Post by goodwine »

msobole1 wrote:Should the last spring be labeled k_n and the last damper be b_n, as opposed to what is written in the book?
Yes, you are right.
Bill Goodwine, 376 Fitzpatrick
sagarwal

Re: Homework 2, due Jaunary 28, 2009.

Post by sagarwal »

Professor:

I am still confused/having trouble with 7.2 Is it appropriate for x1 or x2 to be 0 under the initial condtions and having m1=m2=m3=1?
goodwine
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Re: Homework 2, due Jaunary 28, 2009.

Post by goodwine »

sagarwal wrote:I am still confused/having trouble with 7.2 Is it appropriate for x1 or x2 to be 0 under the initial condtions and having m1=m2=m3=1?
If I'm thinking of the right problem, if x1=0, x2=1 and x3=-1, then the net force on mass 1 will always be zero and the second and third masses will oscillate out of phase with each other.
Bill Goodwine, 376 Fitzpatrick
goodwine
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Re: Homework 2, due Jaunary 28, 2009.

Post by goodwine »

Someone asked me:
I'm stuck on the wording of the very last part of question 7.3. You mention that "...since n is not specified, it is acceptable for the matrix A to contain ellipses." I'm not sure what you mean by ellipses in this context.
Ellipses are the "..." I didn't say what n is, so you need to indicate the intermediate values with those.
Bill Goodwine, 376 Fitzpatrick
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