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Pierce [4] undertook an analysis of the effects of amplifier damping factor on the decay time and frequency-dependent response variations of a closed-box, acoustic suspension loudspeaker system. The results indicated that any damping factor over 10 is going to result in inaudible differences between that and a damping factor equal to infinity.
Damping not based on energy loss can be important in other oscillating systems such as those that occur in biological systems and bikes [4] (ex. Suspension (mechanics)). Damping is not to be confused with friction, which is a type of dissipative force acting on a system. Friction can cause or be a factor of damping.
The logarithmic decrement can be obtained e.g. as ln(x 1 /x 3).Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain.. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
Circuits that will resonate in this way are described as underdamped and those that will not are overdamped. Damping attenuation (symbol α) is measured in nepers per second. However, the unitless damping factor (symbol ζ, zeta) is often a more useful measure, which is related to α by
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
The magnitude of overshoot depends on time through a phenomenon called "damping." See illustration under step response. Overshoot often is associated with settling time, how long it takes for the output to reach steady state; see step response. Also see the definition of overshoot in a control theory context.
The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio by = () A general form is T s = − ln ( tolerance fraction × 1 − ζ 2 ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}}\times {\sqrt {1-\zeta ^{2}}})}{{\text ...
There is no unit designation for transmissibility, although it may sometimes be referred to as the Q factor. The transmissibility is used in calculation of passive hon efficiency. The lesser the transmissibility the better is the damping or the isolation system.