Question

the formula to determine the period of one swing of a simple pendulum is $t = 2pisqrt{\frac{l}{g}}$, where $l$ is the length of the string and $g$ is the acceleration due to gravity. solve the formula to solve for $l$ in terms of $pi$, $t$ and $g$.

Explanation:

Step1: Isolate the square - root term

Divide both sides of the equation $T = 2\pi\sqrt{\frac{L}{g}}$ by $2\pi$. We get $\frac{T}{2\pi}=\sqrt{\frac{L}{g}}$.

Step2: Square both sides

Squaring both sides of the equation $\frac{T}{2\pi}=\sqrt{\frac{L}{g}}$, we have $(\frac{T}{2\pi})^2=\frac{L}{g}$.

Step3: Solve for L

Multiply both sides of the equation $(\frac{T}{2\pi})^2=\frac{L}{g}$ by $g$. So $L = g\times(\frac{T}{2\pi})^2=\frac{gT^{2}}{4\pi^{2}}$.

Answer:

$L=\frac{gT^{2}}{4\pi^{2}}$