# script to show damped oscillator traces

set terminal postscript eps enhanced color font "Times-Italic,24pt" size 12cm,4.5cm dashlength 2.0 
set output 'overdamped.eps'

set border 0
#set tics nomirror
set xrange [0:10]
set yrange [-.65:1.1]
unset xtics
unset ytics


y(t,A,B,beta)=A*exp((-beta-sqrt(beta**2-1))*t)+B*exp((-beta+sqrt(beta**2-1))*t)

set arrow 1 from 0,-.8 to 0,1.3 filled
set arrow 2 from 0,0 to 10.5,0 filled

set label 1 "t" at 10.5,-.15
set label 2 " x{/Times-Roman (}t{/Times-Roman )}" at -1.,1.2
set ylabel " " offset -2,0 

set label 3 "B {/Times-Roman > 0}, B' {/Times-Roman = 0}" at .3,.8
set label 4 "B > B' > 0, {/Symbol b} {/Times-Roman = 2}{/Symbol w}_0" at 2,0.3
set label 5 "B > 0, B' < 0, {/Symbol b}{/Times-Roman = 1.5}{/Symbol w}_0" at 3,-.4

plot y(x,1,0,1.1) lt 1 lc rgb 'red' notitle, \
     y(x,.5,.3,2) lt 1 lc rgb '#c000c0' notitle, \
     y(x,1.3,-.8,1.5) lt 1 lc rgb "blue" notitle