The story goes that in 1581, when Galileo was seventeen,
he noticed that when the lamps in Pisa Cathedral swung,
they did so at the same rate each time, irrespective of
the amplitude of the movement. An area of study was opened
up that was to have important repercussions in many fields
When you make a pendulum its periodicity, that is to say
the time it takes to make one complete oscillation, depends
solely on the length of the wire or rod that supports
it and on the force of gravity in the place where it is
hung. The pendulum swings faster the closer it is to the
centre of the earth, independent of its mass and the width
of its oscillation.
Materials: Brass, steel and walnut wood.
Design: Marc Boada, 1993.
Two pendulums coupled together in a hard-to-detect way?
Look closely at the object and you can see how it can
oscillate from two different points. One, located at the
ends of the little steel rod that we've hung between the
columns, gives the pendulum a maximum oscillation. The
other one, located at the top end of the wire that supports
the pendulum, is slightly shorter. So the real movement
of the pendulum is a combination of the two cycles corresponding
to the two possible lengths.
The movement of the pendulum is the result of the limitations
in the degrees of freedom of the movements of each one
of the oscillation points. That is to say, when it oscillates
on the steel rod it does so only in a plane perpendicular
to a background generated by the oscillation on the end
of the wire. Combined together, these two movements generate
a new, harmonic movement, the result of the sum of both
pendulars. The end of the sphere must barely touch the
sand, which has been smoothed with some type of spatula.
To see it to best effect, the pendulum has to swing hundreds
of times so that the sand takes on a concave form and
the tip only grazes (1 mm) along its path. The effect
is spectacular in raking light, since it is then that
the elliptical shades are perfectly marked in the sand.
Note: we have used emery sand, an abrasive although innocuous
Materials: Brass, bubinga wood and emery sand.
Design: Marc Boada, 1999.
10 seconds of
10 SECONDS OF CAOS
This apparatus is a simple decorative
object. All it is an accumulation of forces and inertias,
a mixture of metals, a delight with no particular meaning,
and an unpredictable operation.
Did I say unpredictable? Only a little chaos, under control,
lasting 10 seconds. Two masses of brass (m1 = 64 grams and
¸1 = 25 millimeters; m2 = 32 grams and ¸2=20 millimeters)
that turn on a common centre can behave like a cushioned
pendulum. They have a tendency to conserve the initial movement
and also its direction, but they have to share this with
the other sphere, subject to different forces and inertias.
The suspension cardan joint on which the spheres are mounted
allows them to rotate around an axis that can point to any
point in space.
When it is pushed smoothly the movable outer ring transmits
a certain energy to the system that is stored in the spheres
(this energy tends to be conserved and it is only reduced
by the various frictions). The pendular behavior of the
spheres then comes into play, each movement generating,
by the principle of action-reaction, a movement in the opposite
direction in the ring: a wonderful transfer of energy in
a closed mechanical system.
In practice it is impossible to predict the position of
the spheres, and the real movement is the superimposition
of the natural periods of oscillation of each one of the
components, of the different masses, of the actual friction
of each pivot, the errors in the of perpendicularity of
the axes, and so on.
Materials: Steel and brass.
Design: Marc Boada, 2002.
The Catacaos is a simple system that he
says with the minimum variables to show a chaotic behavior.
Two masses of brass that they turn on a common center can
be entailed as an attenuated pendulum. They have a trend
to preserve the initial movement and also its address, but
they have to share it with the other mass, subject to forces
and different inertias. The suspension card on the one that
has been gotten on, it allows to turn about one axis that
can note any point of the space to them.
When impulse is given to it with smoothness
one of the exterior mobile rings a certain energy to the
system that is stored in the masses (this energy tends to
be preserved and it only comes down by the different friction)
is transmitted. The pendular behavior of the masses comes
then into action, and every movement of these generates
a movement of contrary meaning, for the beginning of action,
in the rings: a wonderful transfer of energy in a closed
In practice it is impossible to predict
the position of the masses, and the real movement is the
overlap of the natural periods of oscillation of each of
the components, of the different masses, of the specific
friction of every pivot, of the errors of perpendicularity
of the axes, etc.
In this game, two cushioned pendulums oscillate
together. One of them, the main one, has a fixed period
since the masses of which it is made always apply the forces
in the same points. The secondary pendulum has an adjustable
sphere that allows its period to be varied
How to set it in motion? Simply place the axis on the two
concave surfaces of the columns and smoothly push the cylindrical
masses two or three times: chaos result, or not!
Non-chaos? Maybe yes, maybe no; its a simple matter of the
amplitude and periodicity of the oscillations* and of the
adjustment of the secondary pendulum.
* Remember that the Isocronia of the pendulum is a simple
Materials: Iron and brass.
Design: Marc Boada, 2003.
In 1851 the French scientist Jean-Bernar-Leon
Foucault suspended an iron ball weighing 28 kilos with a
steel cable 67 meters in length from the dome of the Pantheon
in Paris, and set it in movement. In order to mark its progress,
he stuck a feather to the ball
and placed a ring of damp sand on the ground underneath.
The spectators were astonished to see that the pendulum
appeared to rotate.
Foucault had demonstrated that the Earth turned on its axis.
MAGNETIC PENDULUM |
Every electrical charge in movement creates a perturbation
in the space named magnetic field, capable of carrying
out motor actions on magnets and burdens in movement.
A burden that carries out a circular movement generates
a magnetic bipolar field, with a North, in which felt
of the vectors of the field they move away from this,
and a South, in which the meaning of the vectors goes
At an atomic scale, any body is format by a continuous
distribution of elemental bipolar moments due to the orbital
displacements of the electrons, but as that generally
they are orientated randomly do not give a clean magnetic
moment, except for the permanent magnets or ferromagnetic
The interaction among magnetic poles of equal sign is
repulsive and among poles of different sign he attractive.
This estate is used in crowd of applications, as for example,
this pendulum. If we throw the ball, it would be expected
it to carry out an oscillatory movement of rating line,
but it happens that the ball finds it impossible to achieve
the vertical position and to pass for the midpoint her,
where an invisible obstacle seems to bounce her. Then
it starts a chaotic dance until it stabilizes. The only
secret is that in the ball and in the platform there are
two hidden magnets with the same faced pole.
In this case two magnets of neodymium, a strange element
of the group of the lanthanides, have been used with a
ferromagnetism among 7 and 10 times superior to of the
the magnets conventional of ferrite.
Part prepared by hand.
Materials: brass, wood and magnets of neodymium
Dimensions: h= 23,5 cm
Design: Marc Boada
This artifact is built in order to generate
chaos and what is unpredictable from the impulse applied
to the octahedron. This finds two concentric rings limited
inside in suspension Cardan. Thus, in a first moment, it
would seem logical that the conservation of the moment of
inertia made turn constantly the octahedron, as in a gyroscope
standing, but quickly the appearance of different moments
of inertia, commuting between the arms of the octahedron
and friction, generates a chaotic and different movement
every time that we make him come into action.
To prepare this divertimento we have chosen
an octahedron, one of the 5 existing regular Platonic or
polyhedral solids, as central figure. These are those that
are limited by identical regular polygons, in which number
of faces contribute in every vertex in the same way. In
the nature this figure can be in some minerals that crystallize
into the cubic system as the fluorite or the magnetite.
Materials: brass and steel.
Dimensions: h = 25cm.
Design: Marc Boada, 2003.
The appeal of a pèndul, its regular
and constant movement, is owed to a subjacent physical phenomenon:
the cyclical transformation of the mechanical energy that
goes from potential in the highest part of the trajectory
to kinetics in the lowest part. The one that makes them
as practical as device, for example, for indicating the
step of the time is this repetitivitat.
This is still more attractive when the pèndul is
composed, that is, when there are two masses associated
rising and descending in the terrestrial gravitational field.
In this there are two masses, one constituted by the pèndula
circular of the center of the instrument and the other one,
less seeress, placed under the one former and in the form
of too much prismatic of steel. Like in all the coupled
pènduls, made mole greater than the other one with
two masses in the one that one is, two normal modus of vibration,
the first in tuning and the other one in opposition are
The real movement will depend on the initial conditions,
the one that departs regrets to sort out the small mass
from its position of equilibrium and to let it oscillate
maybe more interesting from an aesthetic point of view.
In effect, if like this you make it you will be able to
observe how its amplitude of oscillation keeps on being
made every time smaller losing energy while, simultaneously,
the oscillation of the big mass increases for, afterwards,
to transfer again energy towards the small mass and to repeat
Finally, however, every pendulum stops, since the initial
mechanical energy dissipates in the form of heat, showing
like this how the thermodynamics laws always win the game.
Materials: brass and steel.
Dimensions: h = .
Design: Marc Boada, 2006.