Search results
Results from the WOW.Com Content Network
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.
The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. The regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. [ 2 ]
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]
In 1673 Dutch scientist Christiaan Huygens in his mathematical analysis of pendulums, Horologium Oscillatorium, showed that a real pendulum had the same period as a simple pendulum with a length equal to the distance between the pivot point and a point called the center of oscillation, which is located under the pendulum's center of gravity and ...
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
To make this more concrete, consider an idealized pendulum of length 0.5 meters, with an initial displacement angle of 30 degrees; from Eq(1) the period will then be 1.443 seconds. Suppose the biases are −5 mm, −5 degrees, and +0.02 seconds, for L, θ, and T respectively. Then, considering first only the length bias ΔL by itself,
where L is the length of the pendulum and g is the local acceleration of gravity. All pendulum clocks have a means of adjusting the rate. This is usually an adjustment nut (c) under the pendulum bob which moves the bob up or down on its rod. Moving the bob up reduces the length of the pendulum, reducing the pendulum's period so the clock gains ...
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]