Which formula represents the Pendulum Law for the period of a simple pendulum?

• A. P = 2π√(l/g)
• B. P = 2π√(g/l)
• C. P = √(l/g)
• D. P = 2πl/g

Answer: (A)

The main idea is that a simple pendulum behaves like a harmonic oscillator for small swings, so its period comes from solving the equation of motion under that small-angle approximation. You get θ'' + (g/L)θ ≈ 0, which has a angular frequency ω = sqrt(g/L). The time for a full cycle is T = 2π/ω = 2π sqrt(L/g). This shows the period grows with longer length and shrinks with stronger gravity, and it does not depend on the mass of the bob.

So the formula that matches this, including the necessary 2π factor and the square root of length over gravity, is P = 2π sqrt(l/g). The other forms omit the constant or the square root, or mix up the ratio, which would misrepresent the time scale or the dimensions.