The period of a pendulum is given by:
[tex]T=2 \pi \sqrt{ \frac{L}{g} } [/tex]
where L is the pendulum length and g is the gravitational acceleration.
Initially, the period of the pendulum is T=2.00 s while the gravitational acceleration is [tex]g=9.80 m/s^2[/tex]. If we re-arrange the previous equation, we can find the pendulum length:
[tex]L=g \frac{T^2}{(2 \pi)^2}=(9.80 m/s^2) \frac{(2.00s)^2}{4 \pi^2}= 0.994 m[/tex]
Then the same pendulum is moved to another location, and its new period is
[tex]T=1.99863 s[/tex]. Again, by re-arranging the same equation, we can find the value of g (gravitational acceleration) at the new location:
[tex]g=L \frac{(2 \pi)^2}{T^2}=(0.994 m) \frac{4 \pi^2}{(1.99863 s)^2}=9.814 m/s^2 [/tex]
