Question 1190456
equation is:
T = 2 * pi * sqrt(L/g)
divide both sides of the equation by 2 * pi to get:
T / (2 * pi) = sqrt(L/g)
square both sides of the equation to get:
(T / (2 * pi))^2 = L/g
multiply both sides of the equation by g and divide both sides of the equation by (T / (2 * pi))^2 to get:
g = L / ((T / (2 * pi))^2)
this can be simplified to:
g = (L * 4 * pi^2 / T^2


this can be confirmed by randomly assigning a value to g and L.
i chose 64 for L and 16 for g.
i get:
T = 2 * pi * sqrt(L/g) = 2 * pi * sqrt(64/16) = 2 * pi * sqrt(4) = 4 * pi.
the value of T is equal to 4 * pi.


when T = 4 * pi and L = 64, then:
g = L / ((T / (2 * pi))^2) becomes:
g = 64 / ((4 * pi / (2 * pi))^2 which becomes:
g = 64 /  4 which becomes:
g = 16.


since we had originally assigned 16 to g, this confirms the unsimplified formula is correct, given that T = 4 * pi and L = 64.


when T = 4 I pi and L = 64, then:
g = (L * 4 * pi^2 / T^2 bcomes:
g = (64 * 4 * pi^2) / (4 * pi)^2 which becomes:
g = 256 * pi^2 / (16 * pi^2) which becomes:
g = 256 / 16 which becomes:
g = 16.


since we had originally assigned 16 to g, this confirms the simplified formula is correct, given that T = 4 * pi and L = 64.


you can use either the unsimplified formula or the simplified formula.
if they want the answer simplified, then use the simplified formula.


let me know if you have any questions.
theo