Given the function, $y={\displaystyle \underset{n=1}{\overset{?}{}}}sin(nx),$ where $x$ is in radians.

$(1)$ Write an M$-$file to calculate the value of $y$ for $x$ from $0$ to $5$ with an increase of $0\mathrm{.}01.$

$(2)$ Show the result on a $x-y$ plot.

$(3)$ Count how many locations where $y=0.$

Note that some comments are required for your code, and please submit both the code and plot.