Homework for Friday, Oct 9.  (due in class on Friday).

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From the book, Problems:
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 3-4, 3-5, 3-6, 3-7,

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And in addition,
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13) For a moderate or lightly damped harmonic oscillator (i.e., less
than critically damped), calculate AND PLOT the functions for x(t) and
v(t) (position and velocity) for the following initial conditions:
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a) x(0)=x_0, v(0)=0

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b) x(0)=0, V(0)=v_0

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14) Do the same problem for an overdamped oscillator.
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a) x(0)=x_0, v(0)=0
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b) x(0)=0, V(0)=v_0
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15) Do the same problem for a critically damped oscillator
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a) x(0)=x_0, v(0)=0
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b) x(0)=0, V(0)=v_0
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c) Find the initial conditions that lead a critically damped oscillator starting
at x(0)=x_0 to return to the origin most rapidly, e.g., to get within .00001*x_0
in the shortest time!
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If it seems that one of these problems is very similar too, or exactly the same as one
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you did already, that is OK.  Do it anyway again, and hand it in as part of this set
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as if you had never done it before. 


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Reading:
   For what we are doing now now the following reading may be
usefull:
Chapter 3 sec's: 1,2,5,5,6,7,9
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We'll spend some time to really understand how to apply section 9
to the driven oscillator problem...
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You may see some things on phase-diagrams, which we haven't covered
yet but may come back to later.
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