# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'controls.1.png'
set dummy t, y
set key fixed right top vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid
set style increment default
set samples 50, 50
set style data lines
set xrange [ 0.00000 : 13.0000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ * : * ] noreverse writeback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
damp(t) = exp(-s*wn*t)/sqrt(1.0-s*s)
per(t) = sin(wn*sqrt(1.0-s**2)*t - atan(-sqrt(1.0-s**2)/s))
c(t) = 1-damp(t)*per(t)
s = 2.0
wn = 1.0
plot s=.1,c(t),s=.3,c(t),s=.5,c(t),s=.7,c(t),s=.9,c(t),s=1.0,c(t),s=1.5,c(t),s=2.0,c(t)