Equivalent Length Compound Pendulum — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Equivalent Length of Compound Pendulum This formula determines the equivalent length used to calculate the period of oscillation for a compound pendulum, assuming small angle oscillations. Start with the general period formula for a compound pendulum: T = 2 I mgd . Define the equivalent length L eq such that T = 2 L eq /g . Equate the terms to find L eq = I/(md). Substitute the moment of inertia I = k + md 2 (where k is the moment of inertia about the center of mass) into the L eq formula to obtain the specific form. d > 0 k 0 Confusing the equivalent length (L eq) with the actual physical length of the pendulum rod. Assuming the period of oscillation depends only on the mass (m) and not the moment of inertia (k). Ignoring the dependence on the distance 'd' in the denominator of the period formula.