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A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. 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 towards the equilibrium position.
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]
"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.
These early clocks, due to their verge escapements, had wide pendulum swings of 80–100°. In his 1673 analysis of pendulums, Horologium Oscillatorium, Huygens showed that wide swings made the pendulum inaccurate, causing its period, and thus the rate of the clock, to vary with unavoidable variations in the driving force provided by the movement.
A schematic diagram of the Barton's pendulums experiment. First demonstrated by Prof Edwin Henry Barton FRS FRSE (1858–1925), Professor of Physics at University College, Nottingham, who had a particular interest in the movement and behavior of spherical bodies, the Barton's pendulums experiment demonstrates the physical phenomenon of resonance and the response of pendulums to vibration at ...
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 ...
Consider a pendulum of mass m and length ℓ, which is attached to a support with mass M, which can move along a line in the -direction. Let x {\displaystyle x} be the coordinate along the line of the support, and let us denote the position of the pendulum by the angle θ {\displaystyle \theta } from the vertical.
The smaller mass, labelled m, is allowed to swing freely whereas the larger mass, M, can only move up and down. Assume the pivots to be points. The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system ...