Classical Mechanics Homework Assignment #14, due by 9 am Friday November 18 to Krishna’s office Lab 2 3255.
- 9.16. (see Notes for hint and “optional” extension)
- 9.19 (see Notes)
- 9.29 (see Notes)
- 11.6
- 11.9
- 11.25 (see Notes)
Notes
- For problem 9.16, you should find x(t) = AeΩt + Be-Ωt where A and B are arbitrary constants. For an optional extension to this problem that would make for a very nice quiz or exam problem, try this: Assume the distance from the center of the rod out to its edge is L. Assume that at t = 0, x = 0 (the bead is at the pivot point) and v = v0. Determine the amount of time it takes for the bead to reach the end of the rod from its starting point. Consider (though not necessary to actually carry out!) how you might do this from the inertial frame.
- For problem 9.19, the answer in the back is too brief to be useful, as it completely omits adequate discussion of the centrifugal and Coriolis forces.
- For problem 9.29, you may use Eq. (9.73) without deriving it. If you have time, it’s a good opportunity to practice the method used in section 9.8.
- For problem 11.25, you may need to look up the formula for the determinant of a 3×3 matrix. If you do need to look it up, pay attention to its structure. It should look very familiar – does anything cross your mind (hope this is a productive question)? To solve for the eigenvalues, you will wind up with an equation that is cubic in ω2. There are a number of cool ways to solve a cubic equation – see if you have time to learn one that is relevant to solving this problem. Otherwise, you can use MMA to solve this for you.