#############################################################################################
# A gnuplot script to plot the sum of real harmonics as part of Problem 4.1 in UQP.
# Plots with linear combinations of two and six harmonics are shown. 
#
# Y2(x) = cos(2*pi*x/1.5) + cos(2*pi*x/1.6)
# Y6(x) = Y2(x) + cos(2*pi*x/1.7) + cos(2*pi*x/1.8) + cos(2*pi*x/1.9) + cos(2*pi*x/2.0)
#
#          written by thomas l. gibson  September 12, 2013
#############################################################################################
######Initialize Constants
c1 = 2*pi
###### xrange
L0 = 10  # Narrow View
#L0 = 40  # Wide View
############################################################################################
f(x) = 0
Y2(x) = cos(c1*x/1.5) + cos(c1*x/1.6)
Y6(x) = Y2(x) + cos(c1*x/1.7) + cos(c1*x/1.8) + cos(c1*x/1.9) + cos(c1*x/2.0)
#set nokey
set key top left
set title "Finite Sum of Real Harmonics"
set samples 1000
plot [-L0: L0] [-8: 8] Y2(x) t 'Sum of Two Harmonics' lw 2 lc rgb 'red',\
     Y6(x) t 'Sum of Six Harmonics' lw 2 lt 1 lc rgb 'blue',\
     f(x) t '' lw 3 lc rgb 'black'
set xlabel "x"
pause -1 "Hit return to make harmonic_wavepacket.ps or cntl c to exit."
#z(x) = 0
set terminal postscript enhanced
set output "harmonic_wavepacket.ps"
#set nokey
replot
reset
exit