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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 ...
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).
Charge transfer coefficient, and symmetry factor (symbols α and β, respectively) are two related parameters used in description of the kinetics of electrochemical reactions. They appear in the Butler–Volmer equation and related expressions. The symmetry factor and the charge transfer coefficient are dimensionless. [1]
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.
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 ...
model damped unforced oscillations of a weight on a spring. The displacement will then be of the form () = / (). The constant T (= /) is called the relaxation time of the system and the constant μ is the quasi-frequency.
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 ...
Different resonant frequencies can be excited dependent on the position of the support wires, the mechanical impulse and the microphone. The two most important resonant frequencies are the flexural which is controlled by the Young's modulus of the sample and the torsional which is controlled by the shear modulus for isotropic materials.