IMPORTANT NOTE: For FULL credit provide ALL the steps that led you to your answer, and computer generated, fully annotated graphs $($i$.$e$.$ you should include the title of the graph, the names and units of the two axes, and in the case of multiple curves, you should have a legend which shows which curve is which$)$

A wave profile is given as $($ and $x$ in feet and $t$ in seconds$)$:

$(x,t)=$Ccos$[A{k}^{\text{'}}x-t]$

where $C=5ft,$ is the wave frequency, $k^{\text{'}}=0\mathrm{.}05f{t}^{-1},$ and $A$ is a unitless constant.

It is also known that the wave length, $L,$ and the wave period $T$ are related through this relationship ${?}^2$ :

$L=\frac{g{T}^2}{2}$

where $g=32\mathrm{.}2f\frac{t}{se{c}^2}$ is the acceleration of gravity.

$($a$)$ For $A=0\mathrm{.}6$ what are the amplitude, the height, the length, L $,$ the period, T$,$ and the celerity of this wave? In which direction is this wave traveling $($relative to $+x$ direction$)?$ Plot the wave profiles at $t=0sec,\frac{T}{7}sec,$ and $3\frac{T}{7}sec,$ over one wave length $x=0x=LA=-1\mathrm{.}4t=0sec,\frac{T}{7}sec,3\frac{T}{7}secx=0x=Lxmt=0\mathrm{.}5sin(-25x-5t)=-2\mathrm{.}1cos(-15t+6x-\frac{}{5})$