Homework #3

Due by 5 pm Wednesday September 20^th.

Problems mostly from the book

1. 3-1) Truly trivial drill but it sets the stage for
2. 3-2) which will make you extract the equations from the results.
3. 3-7) Bathtub toy physics--a classic kind of problem where you have to show that something produces SHM.
4. 3-18) The question tells you what approximations to make, and this one is all about making approximations.
5. 3-24) This time I recommend using Maple to do the numeric work.
6. 3-42) Another show that this leads to SHM problem.
7. 3-45) Another extracting the equation parameters from the data question.
8. Consider a lightly damped, unit frequency SHO, β = 0.01. Find and plot the output when the oscillator is driven by a square wave acceleration (Force/mass) given by
   F(T)/m = +1 {2nπ <= t < (2n+1)π} and F(t)/m = -1 {(2n+1)&pi <= t < 2nπ}.
   Note that this driving force is periodic with period 1.
   I would like you to try to solve this both analytically and numerically (I suggest Maple) and to compare your results.
9. 3-8) Extra Credit, don't even think about this one unless you have done and are happy with all the others. Beware, this may be a several hour problem. It is worth 0.5% towards the final grade. I include it only as a challenge.