$(7$ points$)$ A simple pendulum experiment is designed to measure the gravitational

acceleration g$.$ The simple pendulum consists of a rigid bob and an inelastic string as

shown below. When the rotational angle $\backslash$theta is kept small, the gravitational acceleration

g$=(4\backslash$pi $^(2)$L$)/($T$^(2)),$ where L is the length of the string and T is the period of oscillation of the

pendulum. The length of the string is measured using a ruler, it is $0\mathrm{.}96$ m with an

uncertainty of $+-0\mathrm{.}01$m$.$ The period of oscillation T is measured using a stopwatch, it is

$1\mathrm{.}95$s with an uncertainty of $+-0\mathrm{.}05$s$.$ U$\_($TT$)$

Find the nominal value and the propagated uncertainty in the estimated

gravitational acceleration g$.$

g$=(4\backslash$pi $^(2)$L$)/($T$^(2))$

L$\_(5$hy$)=0,96$m$+-0\mathrm{.}00$m

T$=1\mathrm{.}95$s$+-0\mathrm{.}05$s

U$\_($g$)=\backslash$sqrt$((($dely$)/(\backslash$gamma $\_(1)))^(2)$v$\_(2)+(($del$\_(1))/($delr$\_(2)))^(2))$