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Plot showing underdamped and overdamped responses of a series RLC circuit to a voltage input step of 1 V. The critical damping plot is the bold red curve. The plots are normalised for L = 1, C = 1 and ω 0 = 1. The differential equation has the characteristic equation, [7] + + =.
An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here damping ratio is always less than one. Critically damped A critically damped response is the response that reaches the steady-state value the fastest without being ...
For example, landing a plane in autopilot: if the system overshoots and releases landing gear too late, the outcome would be a disaster. Critically damped The case where = is the border between the overdamped and underdamped cases, and is referred to as critically damped. This turns out to be a desirable outcome in many cases where engineering ...
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 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 ...
The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called critically damped. If an external time-dependent force is present, the harmonic oscillator is described as a driven oscillator .
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 parameters in the above equation are: controls the amount of damping,; controls the linear stiffness,; controls the amount of non-linearity in the restoring force; if =, the Duffing equation describes a damped and driven simple harmonic oscillator,
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