source('utils.R')

t = seq( 0, 60, length.out=500 )

n = 15
g = u_sub_c( t, 0 )
for( k in 1:n ){
    g = g + (-1)^k * u_sub_c( t, k*pi )
}
#postscript("../../WriteUp/Graphics/Chapter6/sect_4_prob_21_g_t_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( t, g, type='l', xlab='t', ylab='g(t)' )
grid()
#dev.off()


# Plot the solution:
#

t = seq( 0, 60, length.out=1000 )

y = 1 - cos(t)
for( k in 1:n ){
    y = y + (-1)^k * u_sub_c( t, k*pi ) * ( 1 - cos( t - k*pi ) )
}

#postscript("../../WriteUp/Graphics/Chapter6/sect_4_prob_21_y_t_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( t, y, type='l', col='black', xlab='t', ylab='y(t)' )
grid()
#dev.off()