# How do you solve for g in T = 2pi sqrt(L/g)?

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Mar 8, 2018

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

#### Explanation:

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

Divide both sides by $2 \pi$:

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

Square both sides:

$\frac{l}{g} = {T}^{2} / \left(4 {\pi}^{2}\right)$, or:

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

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

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