The formula for the period of a simple pendulum is given by:

$$ T = 2\pi\sqrt{\frac{l}{g}} $$

where:

• T is the period of the pendulum,
• l is the length of the pendulum, and
• g is the acceleration due to gravity.

We need to find g. Rearranging the formula for g, we get:

$$ g = \frac{4\pi^2l}{T^2} $$

Given:

• l = 2 m,
• T = 2 s,

Substituting these values into the equation, we get:

$$ g = \frac{4\pi^2 \times 2}{(2)^2} = 2\pi^2 \, ms^{-2} $$