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The above discussion focuses on a pendulum bob only acted upon by the force of gravity. Suppose a damping force, e.g. air resistance, as well as a sinusoidal driving force acts on the body. This system is a damped, driven oscillator, and is chaotic. Equation (1) can be written as
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.
A harmonograph creates its figures using the movements of damped pendulums. The movement of a damped pendulum is described by the equation = (+),in which represents frequency, represents phase, represents amplitude, represents damping and represents time.
controls the amount of non-linearity in the restoring force; if =, the Duffing equation describes a damped and driven simple harmonic oscillator, γ {\displaystyle \gamma } is the amplitude of the periodic driving force; if γ = 0 {\displaystyle \gamma =0} the system is without a driving force, and
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 ...
"Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. [1] When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.
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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 behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering , chemical engineering , mechanical ...