Homework 4, due October 2, 2013

[goodwine]

Reading: Chapter 4.

Exercises: 4.3, 4.4, 4.6, 4.7, 4.9, 4.12, 4.14 and 4.15.

[jnorby]

For 4.3 part 1), would it be acceptable to leave c1 and c2 in the homogeneous part of the solutions, rather than finding them in terms of x-nought and x-dot-nought? It seems like a lot of algebra otherwise.

[goodwine]

For 4.3 part 1), would it be acceptable to leave c1 and c2 in the homogeneous part of the solutions, rather than finding them in terms of x-nought and x-dot-nought? It seems like a lot of algebra otherwise.

No, but in the grand scheme of things it wouldn't be the craziest decision to skip it and take a very small point penalty.

[jbruns2]

For problem 4.3 part 4, my plot shifts up to 1.5 at r=1. This does not look like the figure of the phase shift in the chapter, so how does the phase shift continue to decrease to less than -1.5 after the ratio becomes greater than 1?

[goodwine]

For problem 4.3 part 4, my plot shifts up to 1.5 at r=1. This does not look like the figure of the phase shift in the chapter, so how does the phase shift continue to decrease to less than -1.5 after the ratio becomes greater than 1?

That's a result of the tan^{-1} function you are using. Check what it's returning by default.

[jsoisson]

Prof. Goodwine,

Would it be a valid assumption for this and future assignments that for where the problem asks to "graph" a solution it is acceptable to turn in a MATLAB plot, and when it asks to "sketch" a solution it is not? Thanks.

[goodwine]

Prof. Goodwine,

Would it be a valid assumption for this and future assignments that for where the problem asks to "graph" a solution it is acceptable to turn in a MATLAB plot, and when it asks to "sketch" a solution it is not? Thanks.

Yes, that's a good way to put it.

[John Hollkamp]

I have two questions: For problem 4.6, should the omegas be different from one another; that is should they have subscripts associated with them? And for 4.9, do we assume the same initial conditions as in problem 4.3 and then found the solution for three different zeta cases?

[goodwine]

I have two questions: For problem 4.6, should the omegas be different from one another; that is should they have subscripts associated with them? And for 4.9, do we assume the same initial conditions as in problem 4.3 and then found the solution for three different zeta cases?

In 4.6 the omegas in the solution correspond to the two different omegas in the forces, so you can think of them as omega_1 and omega_2 (I didn't put subscripts on them to distinguish them from the things you determine, but it's probably clearer to think of it your way). In 4.9 you don't need any initial conditions. The problem is to determine the equations, not to solve them.