A pendulum of length L oscillates with an angular amplitude of θ = 60° and time period T. Let T₀ = 2π√(L/g) be the time period for small angle of oscillations, where g is the acceleration due to gravity. If air resistance is negligibly small and the string remains straight, then which one of the following is correct?

The standard formula T₀ = 2π√(L/g) is derived using the small-angle approximation sin θ ≈ θ. For larger amplitudes like 60°, this approximation breaks down because sin θ < θ, making the restoring force smaller than predicted by the linear approximation. As a result, the actual time period T is slightly greater than T₀. The exact formula involves an infinite series correction: T = T₀[1 + (1/16)θ² + ...], showing that larger amplitudes lead to longer time periods. The mass of the bob does not affect the time period of a simple pendulum. Therefore, T will be slightly greater than T₀.