PHYS 4840 Mathematical and Computational Physics II
 
        Homework #4     Due 2013 March 15

Textbook problems 4.4, 4.8, 4.11, 4.13

For 4.4, please make "x vs t" and "y vs x" plots for three scenarios:
 A=0.5, B=1, x_initial=0.1, y_initial=2
 A=1,   B=3, x_initial=1,   y_initial=1
 A=2,   B=5, x_initial=1,   y_initial=1
In all scenarios please use Nstep=10000 and tau=0.01.

For 4.8, please show me on paper the initial mathematics leading up 
to the code you eventually write.  Hint: do 5 mini-loops, plus the 
outer loop.  Do 6 junction rules (ignore "input" and "output" 
junctions).  This leaves you with 12 equations and 12 unknowns.
The plot in the back of the text assume epsilon=1 Volt.

For 4.11, please use the following values for the spring constants 
and rest lengths:
k=[1 1 4 2]
L=[2 4 3 5]
Also, please use a range of 0<Lw<20 in your plot.  

For both 4.11 and 4.13 please show me the arithmetic leading to your code (i.e., show me your matrix equations).