Question

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

Answer 1

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)`