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 of physics.

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.

 

Hand-made piece.
Materials: Brass, steel and walnut wood.
Dimensions: h=37,5cm.
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 material.

Hand-made piece.
Materials: Brass, bubinga wood and emery sand.
Dimensions: h=28,5cm.
Design: Marc Boada, 1999.

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.

Hand-made piece.
Materials: Steel and brass.
Dimensions: h=20cm.
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 mechanical system.

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 approximation.

Hand-made piece.
Materials: Iron and brass.
Dimensions: h=30cm.
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.

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 towards this.
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 materials.
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.

Hand-made piece.
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 presented.
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 the process.
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.

Hand-made piece.
Materials: brass and steel.
Dimensions: h = .
Design: Marc Boada, 2006.