hw2 solution - 1 PHZ 5156, Computational Physics Homework 2...

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1 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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2 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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hw2 solution - 1 PHZ 5156, Computational Physics Homework 2...

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