u$\_$o $=($h$\_$a$*$k$*$c$)/($sinh$($k$*$H$\_$o$),$ A $=($h$\_$a$*$c$)/$sinh$($k$*$H$\_$o$),$ c$^2=$ g$*$tanh$($k$*$H$\_$o$)/$k $,$ with k$=2$pi$/$wavelength$.$ H$\_$o $=5$m$,$ wavelength$=400$ m$,$ and h$\_$a $=0\mathrm{.}04$ m$.$ Solve for C$,$ A and u$\_$o$.$ and then plot the properties of u$($x$,$y$,$t$)$ as a function of y for x $=0$ and kct $=0,$ pi$/4,$ pi$/2,3$pi$/4,$ pi$,$ and etc up to $2$pi$.$ Comment on the pattern you see. Derive a form for bottom shear stresse tau$\_$o$.$ Show how this vaies in time when x$=0.$ plot together with the plot of u$\_$pb$/$u$\_$o$.$ knowing that u $=$ u$\_$o$\{$cos$[$k$($x$-$ct$)]-($e$^(-$beta$*$y$))*$cos$[$k$($x$-$ct$)+$ beta$*$y$]\}$