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A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
For example, a vibrating rope in 2D space is defined by a single-frequency (1D axial displacement), but a vibrating rope in 3D space is defined by two frequencies (2D axial displacement). For a given amplitude on the modal variable, each mode will store a specific amount of energy because of the sinusoidal excitation.
A 2019 study of automatic pendulum movements using a motion capture system showed that pendulum effect is produced when the fingers holding the pendulum generate an oscillating frequency close to the resonant frequency of the pendulum. At an appropriate frequency, very small driving movements of the arm are sufficient to produce relatively ...
Frequency illusion is common in the linguistic field. Zwicky, who coined the term frequency illusion, is a linguist himself. He gave the example of how linguists "working on innovative uses of 'all,' especially the quotative use," believed their friends used the quotative "all" in conversation frequently.
The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. Moreover, the Duffing system presents in the frequency response the jump resonance phenomenon that is a sort of frequency hysteresis behaviour.
In mathematics, more specifically in dynamical systems, the method of averaging (also called averaging theory) exploits systems containing time-scales separation: a fast oscillation versus a slow drift. It suggests that we perform an averaging over a given amount of time in order to iron out the fast oscillations and observe the qualitative ...
Brainwave entrainment is a colloquialism for 'neural entrainment', [25] which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of external stimuli, such as a sustained acoustic ...