Question

The formula to determine the period of one swing of a simple pendulum is T=2\pi\sqrt{\frac{L}{g}},T=2π g L ​ ​ , where LL is the length of the string and gg is the acceleration due to gravity. Solve the formula to solve for LL in terms of \pi,π, TT and g.G.

Answer 1

L = (T² × g) / 4π²

Explanation:

T = 2π√L/g

Where,

L = length of the string

g = acceleration due to gravity

T = 2π√L/g

square both sides of the equation to eliminate the square root

T² = (2π)²√(L/g)²

T² = (2π)²(L/g)

(2π)²

= 2π × 2π

= 4π²

T² = 4π²(L/g)

Multiply both sides by g

T² × g = 4π²(L/g) × g

T² × g = 4π²L

Divide both sides by 4π² to get L

L = (T² × g) / 4π²