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

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

You want to solve for $g$ in terms of $T$, $\pi$, and $L$. Let's do that step by step:

Step 1: Square both sides to eliminate the square root.

$T^2 = (2\pi)^2 \cdot \frac{L}{g}$

This simplifies to:

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

Step 2: Solve for $\frac{L}{g}$.

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

Step 3: Isolate $g$.

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

Thus, the acceleration due to gravity $g$ in terms of $T$ and $L$ is:

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

This is the formula for $g$ in terms of the pendulum length $L$ and the period $T$.

Would you like further clarification on this?

Here are five related questions you can explore:

1. How does the length of the pendulum affect the period of the swing?
2. What happens to the value of $g$ if the period doubles?
3. How is this formula derived from the forces acting on a pendulum?
4. If the period is measured in seconds, what are the units of $g$?
5. How can we apply this formula in an experiment to measure $g$?

Tip: For accurate pendulum experiments, ensure small angles of displacement to avoid deviations from the simple pendulum formula.