Homework #4

Due in class Friday September 21^st.

Problems mostly from the book

1. 3-21) Hint: you know the solution so you can figure out the equation of the line on the phase plot.
2. 3-25) Maple time!
3. 3-43) A classic kind of show that this gives SHO for small oscillations problem.
4. 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.
5. 6-2) You know the answer, now prove it!
6. 6-4) And, as you know, a geodesic is the shortest distance curve.
7. 6-5) This is another version of the soap bubble surface.
8. 6-6) Another one to make you work through a chapter example.
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.