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The effect of varying damping ratio on a second-order system. The damping ratio is a parameter, usually denoted by ζ (Greek letter zeta), [7] that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator ...
A second-order low-pass filter with a very low quality factor has a nearly first-order step response; the system's output responds to a step input by slowly rising toward an asymptote. A system with high quality factor (Q > 1 / 2 ) is said to be underdamped. Underdamped systems combine oscillation at a specific frequency with a decay of ...
The tuning application, for instance, is an example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning that any voltage or current in the circuit can be described by a second-order differential equation in circuit analysis. The three circuit elements, R, L and C, can be combined in a number of different ...
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.
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.
Settling time depends on the system response and natural frequency. The settling time for a second order , underdamped system responding to a step response can be approximated if the damping ratio ζ ≪ 1 {\displaystyle \zeta \ll 1} by T s = − ln ( tolerance fraction ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln ...
Overdamped (ζ > 1): The system returns (exponentially decays) to steady state without oscillating. Larger values of the damping ratio ζ return to equilibrium more slowly. Critically damped (ζ = 1): The system returns to steady state as quickly as possible without oscillating (although overshoot can occur if the initial velocity is nonzero ...
For second-order systems, the percentage overshoot is a function of the damping ratio ... The damping ratio can also be found by