A $52\mathrm{.}9$ cm$-$long pendulum takes $1\mathrm{.}50$ minutes to undergo $62\mathrm{.}3$ complete oscillation cycles.

$($a$)$

Compute the pendulum's period $($in s$).$

s

$($b$)$

Determine the acceleration due to gravity $($in m$/$s$2)$ at the place where the pendulum is located.

m$/$s$2$