Answer to Question #317933 in Mechanics | Relativity for Lipika

Question

Derive an expression for the logarithmic decrement of a damped oscillator.

Answer 1

Answer

The logarithmic decrement represents the rate at which the amplitude of a free damped vibration decreases. It is defined as the natural logarithm of the ratio of any two successive amplitudes. It is found from the time response of underdamped vibration.

So it's formula is

$A=ln(\frac{x_1}{x_3})$