A simple pendulum with a length of $2\mathrm{.}23m$ and a mass of $6\mathrm{.}69kg$ is given an initial speed of $1\mathrm{.}46\frac{m}{s}$ at its equilibrium position.

$($a$)$ Assuming it undergoes simple harmonic motion, determine its period $($in s$).$

$($b$)$ Determine its total energy $($in J$).$

$($c$)$ Determine its maximum angular displacement $($in degrees$).($For large $v,$ and$/$or small $\frac{?}{?},$ the small angle approximation may not be good enough here.$)$ where $10?$