Question

The formula to determine the period of one

swing of a simple pendulum is
L
T = 2√, where L is the length of the
string and g is the acceleration due to
gravity. Solve the formula to solve for g in
terms of T, T and L.

Answer 1

To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:

First, we divide both sides by 2π:

T/2π = √(L/g)

Then, we square both sides:

(T/2π)² = (L/g)

Then, we multiply both sides by g^2 :

(T^2/4π^2) = L

Finally, we divide both sides by L:

(T^2/4π^2 * L) = g

So the formula for g in terms of T, L is g = (T^2/4π^2 * L)

Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.