Time Period Of Simple Pendulum — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Time Period of Simple Pendulum Valid only for small angular displacements (typically < 10 degrees) where sin(theta) ≈ theta. Write the equation of motion using torque: τ = -L(mg sin θ). Apply Newton's second law for rotation: τ = Iα. Equate and simplify assuming point mass (I = mL²): mL²α = -mgL sin θ. Apply small angle approximation: sin θ ≈ θ. Recognize the SHM differential equation form: d²θ/dt² = -(g/L)θ. Identify angular frequency ω = sqrt(g/L) and Period T = 2π/ω. The string must be massless and inextensible. The bob is treated as a point mass. Motion must occur in a vertical plane. No air resistance or friction at the pivot. Mass of the bob affects the period (it does not). Amplitude affects the period significantly (only true for large angles, not in the simple harmonic limit). Length is measured to the top or bottom of the bob (it is measured to the center of mass).