The formula to determine the period of one swing of a simple pendulum is T = 2
g, Where
L is the length of the string and g is the acceleration due to gravity. Solve the formula to solve for g in terms of i, T and L.

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.

The formula to determine the period of one swing of a simple pendulum is T = 2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. Solve the formula to find g in terms of T and L.

Learn how to solve for the acceleration due to gravity (g) using the period (T) and length (L) of a pendulum. This solution involves algebraic manipulation of the pendulum period formula T = 2π√(L/g). Suitable for high school students in Grades 9-12.

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