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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 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.
The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
= is called the "damping ratio". Step response of a damped harmonic oscillator; curves are plotted for three values of μ = ω 1 = ω 0 √ 1 − ζ 2. Time is in units of the decay time τ = 1/(ζω 0). The value of the damping ratio ζ critically determines the behavior of the system. A damped harmonic oscillator can be:
Zero damping will produce a maximum response. Very high damping produces a very boring SRS: A horizontal line. The level of damping is demonstrated by the "quality factor", Q which can also be thought of transmissibility in sinusoidal vibration case. Relative damping of 5% results in a Q of 10.
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However, the unitless damping factor (symbol ζ, zeta) is often a more useful measure, which is related to α by = . The special case of ζ = 1 is called critical damping and represents the case of a circuit that is just on the border of oscillation. It is the minimum damping that can be applied without causing oscillation.
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