By definition, the formula of the period of a pendulum is given by:
[tex] T = 2\pi\sqrt {\frac{l}{g}} [/tex]
From here, we must clear the value of l.
We have then:
[tex] \frac{T}{2\pi} = \sqrt {\frac{l}{g}} [/tex]
Raising both members to the square we have:
[tex] \frac{T ^ 2}{4 \pi^2} = \frac{l}{g} [/tex]
Then, passing gravity to multiply, we have:
[tex] l = \frac{gT^2}{4\pi^2} [/tex]
Answer:
When clearing we have:
[tex] l = \frac{gT ^ 2}{4\pi^2} [/tex]
