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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 damped, driven pendulum is a chaotic system. ... he proved that if a pendulum is driven by an impulse that is symmetrical about its bottom equilibrium position, ...
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 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 ...
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 ...
Phase portrait of damped oscillator, with increasing damping strength. All real-world oscillator systems are thermodynamically irreversible. This means there are dissipative processes such as friction or electrical resistance which continually convert some of the energy stored in the oscillator into heat in the environment. This is called damping.
A familiar experience of both parametric and driven oscillation is playing on a swing. [1] [2] [3] Rocking back and forth pumps the swing as a driven harmonic oscillator, but once moving, the swing can also be parametrically driven by alternately standing and squatting at key points in the swing arc. This changes moment of inertia of the swing ...