t_max = 2.5
t = seq(0, t_max, length.out=1000 )
y = ( 1/(8*sqrt(31)) ) * exp(-2*t) * sin( 2 * sqrt(31) * t )

# Find the time tau after which lu(t)| < 0.01 for all t>tau
#
y_thresh = 0.01/12 # in feet
below_t = abs(y) < y_thresh
# Walk backwards until we get the first FALSE:
#
t_index = length(y)
while( below_t[t_index] ){
    t_index = t_index-1
}
tau = t[t_index+1]
print(sprintf('tau= %.3f', tau))

#postscript("../../WriteUp/Graphics/Chapter3/sect_7_prob_10_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( t, y, type='l', main='problem 10' )
abline(v=t[t_index+1], col='black')
abline(h=c(-y_thresh, y_thresh), col='red')
grid()
#dev.off()