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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.
The movement of a damped pendulum is described by the equation = (+), in which represents frequency, represents phase, represents amplitude, represents damping and represents time. If that pendulum can move about two axes (in a circular or elliptical shape), due to the principle of superposition, the motion of a rod connected to the bottom ...
For example, two pendulum clocks (of identical frequency) mounted on a common wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665. [ 2 ] The apparent motions of the compound oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description ...
An important concept is the equivalent length, , the length of a simple pendulums that has the same angular frequency as the compound pendulum: =:= = Consider the following cases: The simple pendulum is the special case where all the mass is located at the bob swinging at a distance ℓ {\displaystyle \ell } from the pivot.
Moreover, a double pendulum may exert motion without the restriction of only a two-dimensional (usually vertical) plane. In other words, the complex pendulum can move to anywhere within the sphere, which has the radius of the total length of the two pendulums. However, for a small angle, the double pendulum can act similarly to the simple ...
"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.
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in ...