PROBLEM SET 1 COMMENTS - SPRING 2003

       1.1 (b), (c):  There can't be much doubt, but for the record,
         "tau" is to be taken as a real constant.

       1.3:  Of course, when the indices on the oscillators run from 0
         to N, there are N+1 oscillators.
	 In (b), "Show" is sort of vague, reflecting the fact that
         there are many ways, of varying complexity (not really a pun)
         to show the desired result.
	 In (c), that's not a typo;  it could be written as 2x_0+x_1.

       1.4:  Okay, the figure is not an equilateral triangle, but
         you'll want to make your own figure anyway. The "... light
         wire elements ..." are to be taken as being rigid;  the
         triangle retains its shape as it moves.

       1.5 (a):  If you use the hint, the kinetic energy of the
         rolling ball is not trivial;  it's not hard, but there's some
         neat kinematics involved, something not always seen at the
         8.01 level.

       1.5 (b):  The quantity y(t) is not defined explicitly;  do what
         you must.  I get this to work best if I take y(t) to be the
         displacement of the liquid in either side of the tube from
         equilibrium;  of course, when one side goes up the other goes
         down, and it turns out not to matter which side you choose.
         As in part (a), it seems easiest to use energy
         considerations.  If you do this, though, keep in mind that
         unless the densities are equal, at equilibrium the heights in
         the two tubes will not be the same.
	 (I have not yet found a "slick and easy" way to do this one.)