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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 ...
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.
In chemical kinetics, relaxation methods are used for the measurement of very fast reaction rates. A system initially at equilibrium is perturbed by a rapid change in a parameter such as the temperature (most commonly), the pressure, the electric field or the pH of the solvent. The return to equilibrium is then observed, usually by ...
It corresponds to the underdamped case of damped second-order systems, or underdamped second-order differential equations. [6] Damped sine waves are commonly seen in science and engineering, wherever a harmonic oscillator is losing energy faster than it is being supplied. A true sine wave starting at time = 0 begins at the origin (amplitude = 0).
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.
The Q factor or quality factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, and characterizes the bandwidth of a resonator relative to its center frequency. [23] [24] A high value for Q indicates a lower rate of energy loss relative to the stored energy, i.e., the system is lightly damped.
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 ...
It offers a concrete interpretation of the pre-exponential factor A in the Arrhenius equation; for a unimolecular, single-step process, the rough equivalence A = (k B T/h) exp(1 + ΔS ‡ /R) (or A = (k B T/h) exp(2 + ΔS ‡ /R) for bimolecular gas-phase reactions) holds. For a unimolecular process, a negative value indicates a more ordered ...