Waves and Oscillations - Damped Harmonic Oscillator : Logarithmic Decrement
Amplitude of a damped simple harmonic oscillator decays with time asymptotically. This decrement of the oscillator is measured in terms of a very useful quantity known as Logarithmic Decrement. Logarithmic decrement is defined as the natural logarithm of the ratio between the two successive amplitudes on the same side of the equilibrium position of a damped simple harmonic oscillator separated by one full period. The expression for this logarithmic decrement has been obtained. It is found that the logarithmic decrement is proportional to the damping coefficient of the medium. Therefore in case of a free oscillator it’s zero.