PHYS 4840 Mathematical and Computational Physics II
 
        Homework #3     Due 2013 February 26

Textbook problems 3.3, 3.7, 3.12, 3.15, 3.18

3.3: 
Please use an initial radial distance of 1 AU, an initial tangential
velocity of 3pi/2 AU/yr, and a time step of 0.005 yr.  
Please show me a plot of the orbit.

3.7:
Please use v=[0 1 0] m/s, E=[0 1 0] V/m, B=[0 0 1] T, tau=10^{-14} s.
Please show me a plot of y vs x.

3.12:
Please use an initial radius of 1 AU, an initial tangential velocity of 
2pi AU/yr, and a time step of 0.01 yr.  Have the external force act in 
the positive x-direction.
Please show me a plot of several orbits in addition to the plot of
L vs t.

3.15:
Please use an initial radius of 1 AU and an initial tangential velocity
of 2pi AU/yr.  Please make a plot showing several orbits, in addition to
a plot of KE, PE, & total E vs time.  Warning: use 'norm(v)' instead of 'abs(v)' for |v|.

3.18:
Please use an initial angle of 10 degrees.
In addition to what is required, please also compute the period of the
pendulum and the stiff spring for each value of the spring constant.
I would like to see six different plots:
3.18a: y-vs-x for k=10^2 N/m
3.18b: y-vs-x for k=10^3 N/m
3.18c: y-vs-x for k=10^4 N/m
3.18d: y-vs-x for k=10^5 N/m
3.18e: y-vs-x for k=10^6 N/m
3.18f: average time step vs spring constant