Functions of Space and Time. Consider the expression below for the electric field of a $100$ MHz wave.

a$)$ Use MATLAB to make snapshot plots of E$($z$,$ t$)$ at three different times: t $=0,$ t $=2\mathrm{.}5$ nsec$,$ t $=5$ nsec for z

from $0$ to $20$ meters. Make all three plots on separate axes part of one figure. Make your y $$axis limits

$[-6,6]$ and show grid lines. The title of each subplot should display the time. Hint: you will need the

following MATLAB commands: subplot, plot, grid on$,$ title

b$)$ Now we want to make an on screen animation of E$($z$,$ t$)$ from t $=0$ to t $=100$ nsec in $0\mathrm{.}25$ nsec increments.

To do this you need to write a for loop and continuously plot E$($z$,$ t$)$ for z from $1$ to $20$ meters and

different values of t$.$ To make each frame visible put pause$(\mathrm{.}2)$ in your for loop just after the plot

command, this will pause the code execution for $0\mathrm{.}2$ seconds. Try to make each title update automatically

$)$cos$(),(0$ ztEtzE x

b

w $-=$ a

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$6$

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$210010$ ; $2\mathrm{.}0944$

E z t t z

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w p

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$==$