Prove that T=2π√l/g with little explanatory sentences
To prove T=2π√l/g, we can start with the formula for the period of a simple pendulum, which is T=2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity.
First, we can rearrange the formula to isolate T:
T=2π√(l/g)
Next, we can square both sides of the equation to get rid of the square root:
T^2 = (2π√(l/g))^2
T^2 = (2π)^2(l/g)
T^2 = 4π^2(l/g)
Finally, we can simplify by multiplying both sides by g and then taking the square root to get T by itself:
T = √(4π^2(l/g) * g)
T = 2π√l/g
Therefore, we have proven that T=2π√l/g.