Homework #4

Due in class Friday October3^rd.

Problems mostly from the book

1. 3-43) A classic kind of show that this gives SHO for small oscillations problem.
2. 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)π <= 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.
3. 6-2) You know the answer, now prove it!
4. 6-4) And, as you know, a geodesic is the shortest distance curve.
5. 6-5) This is another version of the soap bubble surface.
6. 6-6) Another one to make you work through a chapter example.
7. 6-11) To start you thinking about constraints.
8. 6-15) Straight drill.