Logarithmic Decrement Formula — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Logarithmic Decrement Formula Used exclusively for analyzing the amplitude decay of a system undergoing damped Simple Harmonic Motion (SHM). The amplitude of damped SHM decays exponentially: A(t) = A 0 e - t . The ratio of successive amplitudes is found by setting time intervals equal to the period T d : A n A n+1 = e T d . Taking the natural logarithm yields the logarithmic decrement: = ( A n A n+1 ) = T d . Since the damped angular frequency is d = 2 T d , T d = 2 d (dimensionless). A n > 0 A n+1 > 0 The system must be under damping (underdamped case). Confusing the logarithmic decrement ( , dimensionless) with the damping coefficient ( , s -1 ). Assuming the decay is linear instead of exponential/sinusoidal. Using the formula for the natural frequency ( ) instead of the damped frequency ( d).