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The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by ¨ + ˙ + + = (), where the (unknown) function = is the displacement at time t, ˙ is the first derivative of with respect to ...
Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or damped sinusoids. This allows the estimation of frequency, amplitude, phase and damping components of a signal.
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 ...
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
This is called the damped resonance frequency or the damped natural frequency. It is the frequency the circuit will naturally oscillate at if not driven by an external source. The resonance frequency, ω 0 , which is the frequency at which the circuit will resonate when driven by an external oscillation, may often be referred to as the undamped ...
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 ...
Near the origin = =, the system is unstable, and far from the origin, the system is damped. The Van der Pol oscillator does not have an exact, analytic solution. [ 13 ] However, such a solution does exist for the limit cycle if f ( x ) in the Lienard equation is a constant piece-wise function.
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.