The formula to determine the period of one swing of a simple pendulum is T=2pi sqrt ((L)/(g)) . where L is the length of the string and g is the acceleration due to gravity.. Solve the formula to solve for D in terms of pi T and g.

To solve the formula for L in terms of T, π, and g, we can follow these steps:<br /><br />Given formula: $T = 2\pi \sqrt{\frac{L}{g}}$<br /><br />Step 1: Square both sides of the equation to eliminate the square root.<br />$T^2 = (2\pi)^2 \cdot \frac{L}{g}$<br /><br />Step 2: Simplify the equation.<br />$T^2 = 4\pi^2 \cdot \frac{L}{g}$<br /><br />Step 3: Multiply both sides of the equation by g to isolate L.<br />$T^2 \cdot g = 4\pi^2 \cdot L$<br /><br />Step 4: Divide both sides of the equation by $4\pi^2$ to solve for L.<br />$L = \frac{T^2 \cdot g}{4\pi^2}$<br /><br />Therefore, the formula for L in terms of T, π, and g is:<br />$L = \frac{T^2 \cdot g}{4\pi^2}$