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.
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 ...
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 ]
If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the string is constrained to be tangent to one of its arches, and the pendulum's length L is equal to that of half the arc length of the cycloid (i.e., twice the diameter of the generating circle, L = 4r), the bob of the pendulum also traces a cycloid path.
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
The pendulum swings with a period that varies with the square root of its effective length. For small swings the period T, the time for one complete cycle (two swings), is = 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.
In 1673 Huygens, having already developed a clock based on the pendulum, proposed to use the length of the pendulum arm for an international unit of length. [2]: 35 The length of a seconds pendulum was determined (in toises) by Marin Mersenne in 1644. In 1660, the Royal Society proposed that it be the standard unit of length.
In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that F n (G) is isomorphic to G. [1] For example, every graph is periodic with respect to the complementation operator , whereas only complete graphs are periodic with respect to the operator ...