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PHZ 5156, Computational Physics
Homework 2 Solution
September 13, 2005
Problem 1 (Garcia 1.23)
(a)
v = 2
π
r/T
with r = Rcos40 and T=24*3600 s gives v=3.553076903 x10
2
m/s.
(b)
a = v
2
/r = 2.583870440 x 10
2
m/s
2
.
(c)
a' is the same with R replaced by R+2m=6378002 m. This gives
v’ = 2.553078017
x 10
2
m/s
a’ = 2.583871249
x 10
2
m/s
2
a’ –a = 8.090000000
x 10
9
m/s
2
This is accurate at most to three places (8.09).
This is repaired by canceling some terms using algebra:
a = v
2
/r = (2
π
/T)
2
R cos40
a’ = same with R replaced by R+2m
hence
a’ – a = (2
π
/T)
2
(2m)cos40 = 8.102447279 x 10
9
m/s
2
This is exact to the number of places shown. Can see that the first approach was
only accurate to two decimal places.
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Problem 2
Python code
# HW2, problem 3.
# Approximate the derivative of f(x)=exp(2x) at x=3
# using the FS and CS approximations. Plot the results.
# MDJ 9/13/05
from scipy import *
import Gnuplot,Gnuplot.funcutils
g = Gnuplot.Gnuplot(debug=0)
g('set terminal aqua')
# Array of step sizes h
h=10.**arange(20,0)
# Calculate for x=3
x = 3.
exact = 2.*exp(2.*x)
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 Fall '08
 Johnson,M

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