Question $\backslash$# $1(11$ points$)$ from $($slide $\backslash$#$8,$ lecture $10).$

Create a vector $\backslash ($ t $\backslash )$ that spans two periods of a sine wave with a frequency of $\backslash ($ f$=10\backslash$mathrm$\{$~Hz$\}\backslash )$ using $10$ equally spaced data points per period $(2$ points$)$

Hint: The period $\backslash ($ T $\backslash )$ is given by $\backslash ($ T$=1/$ f$=0\mathrm{.}1\backslash )$ seconds, so set $\backslash ($ t $\backslash )$ to cover $0\mathrm{.}2$ seconds $($two periods$),$ resulting in a total of $20$ points. Calculate $\backslash ($ y$=\backslash$sin $(2\backslash$pi f t$)\backslash )$

Set up a figure with three vertical subplots. In each subplot:

$-$ Use a red line with circle markers.

$-$ Set the y$-$axis limits to fully encompass the entire range of the signal.

$1.$ In the first subplot, plot y versus t$.(1$ point$)$

$2.$ In the second subplot, generate a vector of random errors as RE $=2*$ rand$(1,$ length$($t$))$ and plot $\backslash ($ y$+$R E $\backslash )$ versus $\backslash ($ t $\backslash ).(1$ point$)$

$3.$ In the third subplot, create an error bar plot of $\backslash ($ y $\backslash )$ versus $\backslash ($ t $\backslash )$ using errorbar with RE as the error. $(1$ point$)$

Ensure each subplot includes a title $($incorporate $\backslash$pi in the title$)$ and labeled axes $(6$ points$).$