A pendulum wave is an elementary physics demonstration and

kinetic art Kinetic art is art from any medium that contains movement perceivable by the viewer or that depends on motion for its effects. Canvas paintings that extend the viewer's perspective of the artwork and incorporate multidimensional movement are ...

comprising a number of uncoupled

simple pendulum A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate i ...

s with

monotonic In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of ord ...

ally increasing lengths. As the pendulums oscillate, they appear to produce travelling and

standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect t ...

s, beating, and random motion.Harvard Natural Sciences Lecture Demonstrations
''Pendulum Waves''
/ref>

History

Ernst Mach Ernst Waldfried Josef Wenzel Mach ( ; ; 18 February 1838 – 19 February 1916) was an Austrian physicist and philosopher, who contributed to the understanding of the physics of shock waves. The ratio of the speed of a flow or object to that of ...

designed and constructed the first pendulum wave demonstration around 1867 at Charles-Ferdinand University in Prague. In the

Czech Republic The Czech Republic, also known as Czechia, and historically known as Bohemia, is a landlocked country in Central Europe. The country is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the south ...

, the demonstration is called . Eric J. Heller at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

suggested the use of the demonstration to simulate quantum revival. In 2001, two

University of Minnesota Morris The University of Minnesota Morris (UMN–Morris) is a public liberal arts college in Morris, Minnesota, United States. It is part of the University of Minnesota system and was founded in 1960 as a public, co-educational, residential liberal a ...

researchers have derived a continuous function explaining the patterns in the pendulums using an extension to the equation for traveling waves in one dimension, and showed that their cycling arises from aliasing of the underlying continuous function. In 2020, illusionist Kevin McMahon, incorporated a massive pendulum wave apparatus, supposedly with flaming

cannonball A round shot (also called solid shot or simply ball) is a solid spherical projectile without explosive charge, launched from a gun. Its diameter is slightly less than the bore of the barrel from which it is shot. A round shot fired from a lar ...

s, as a stunt in

Britain's Got Talent (series 14) The fourteenth series of British talent competition programme '' Britain's Got Talent'' was broadcast on ITV, but in two parts as a result of the COVID-19 pandemic in the United Kingdom during that year which affected production on the progra ...

under the stage name Kevin Quantum.

Design

The lengths of the pendulums are set such that in a given time ''t'', the first pendulum completes ''n'' oscillations, and each subsequent one completes one more oscillation than the previous. As all pendulums are started together, their relative phases change continuously, but after time ''t'', they come back in sync and the sequence repeats. For small perturbations, the period of a pendulum is given by :

T = 2 \pi \sqrt

where ''L'' is the length of the pendulum and ''g'' is the standard acceleration due to gravity. As is the period of a pendulum completing ''n'' oscillations in ''t'', :

\begin
\frac  & = 2 \pi \sqrt \\
\therefore L & = g \Big( \frac \Big)^2 \\
\end

A common choice of ''t'' is 60 seconds. Thus, for ''g'' ≈ 9.8 ms⁻², :

L \approx \frac \; \text

Parameters of the
pendulum wave in
the animation above

{{wide image, pendulum_wave_graph.svg, 1200px, Timeline of the pendulum wave in the animation above

References

Pendulums Kinetic art

History

Design

See also

References