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The damping ratio is a measure describing how rapidly the oscillations decay from one bounce to the next. The damping ratio is a system parameter, denoted by ζ ("zeta"), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1).
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 ...
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 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 ...
The underdamped response is a decaying oscillation at frequency ω d. The oscillation decays at a rate determined by the attenuation α. The exponential in α describes the envelope of the oscillation. B 1 and B 2 (or B 3 and the phase shift φ in the second form) are arbitrary constants determined by boundary conditions. The frequency ω d is ...
Damped oscillators are created when a resistive force is introduced, which is dependent on the first derivative of the position, or in this case velocity. The differential equation created by Newton's second law adds in this resistive force with an arbitrary constant b. This example assumes a linear dependence on velocity.
Damped oscillation is a typical transient response, where the output value oscillates until finally reaching a steady-state value. In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state. The transient response is not necessarily tied to abrupt ...
A wave can be longitudinal where the oscillations are parallel (or antiparallel) to the propagation direction, or transverse where the oscillations are perpendicular to the propagation direction. These oscillations are characterized by a periodically time-varying displacement in the parallel or perpendicular direction, and so the instantaneous ...