Homework 2, due Jaunary 28, 2009.

[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.

[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]

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.

[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]

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.

[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]

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.

[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.