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T=2πlg⎯⎯⎯√. This is the formula for the period t of a pendulum of length l. Solve this formula for l.

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By definition, the formula of the period of a pendulum is given by:


T = 2\pi\sqrt {(l)/(g)}

From here, we must clear the value of l.

We have then:


(T)/(2\pi) = \sqrt {(l)/(g)}

Raising both members to the square we have:


(T ^ 2)/(4 \pi^2) = (l)/(g)

Then, passing gravity to multiply, we have:


l = (gT^2)/(4\pi^2)

Answer:

When clearing we have:


l = (gT ^ 2)/(4\pi^2)

User Adriano Monecchi
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