Question 430101
equation, if i understand you correctly, is:


T = 2 * pi * sqrt(1/g)


divide both sides of this equation by 2 * pi to get:


(T/(2*pi) = sqrt(1/g)


square both sides of this equation to get:


(T/(2*pi)^2 = (1/g)


multiply both sides of this equation by g and divide both sides of this equation by (T/(2*pi)^2 to get:


g = 1 / ((T/2*pi)^2)


this is equivalent to:


g = 1 / ((T^2)/(2*pi)^2) which is equivalent to:


g = (2*pi)^2 / (T^2)


note that, in general, 1/(a/b) = (1*b)/a = (b/a).


if you know the value of T, then you can find the value of g.


Assume T = 2, then, using the equation of g = (2*pi)^2 / (T^2), you will get g = 9.869604401


If you plug the value of T and the value of g in your original equation, then it should be true, assuming we converted the equation correctly.


your original equation is:


T = 2 * pi * sqrt(1/g)


replace T and g with their respective values and you get:


2 = 2 * pi * sqrt (1/9.869604401)


solve this equation to get:


2 = 2, confirming that the value for g, when T = 2, is good.