Epilogue engaged (natural extract from "Telegramática Recopilatórica II")
was once an astronaut walking on Mars and picked up a stone. Once inside the ship took the stone from the box (by the way, not just any box) showed it to another astronaut who walked with him and began to look (finally, after all, not just any rock). Apparently our astronaut had the flu and sneezed uncontrollably on the stone.
They went to Mars.
The trip was a total failure, the spacecraft lost its way back and astronauts died of starvation after eleven years of wandering there.
For the thousand and eleven years after the ship miraculously came back to earth along with the bodies pure-bone-pure-linen and stones collected for that time (Of course, it would have more technology now).
stones were studied: after more than a thousand years this was the greatest day in human history: Scientists have discovered something fascinating : had something very similar to the flu more than ten thousand years! living on Mars ...
and s mple m is a small loop suspended by a thread in ideally ex t ensible and without weight (length " l), set in turn to a vig to horizontal at rest.
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pendular movement. Descomponemo s strength or weight of bj eto into two components perpendicular ent re itself: direction of movement ( tangent to the curve path) and the dire ction thread. to latter component is canceled
with tension uerda c is the force applied to the thread up weight. Ra Mane that the resultant force acting on the body is the tangential component cial weight "p t ."
isochronous LAW OF PENDULUM
formulas of the period and frequency of the pendulum (5) and (6) suggest that these quantities depend only the wire length and the acceleration of gravity.
1)
The period T of a pendulum is independent and pendulum mass:
Whatever the value of the pendulum mass "m", the period "T" is constant (for the same length of thread "l" and in the same place on earth). 2) The period T of a pendulum is independent of the amplitude of the oscillation:
This is true for angles maximum oscillation " to" less than 15 °, as already cited, since for larger angles the approximation made in (7) shows differences greater than 1%. If the same spot on earth (g = constant) are measured periods of two pendulums of different lengths l
SOUND WAVES AND A wave is a disturbance that moves or propagates in a medium or even in a vacuum. Despite the diverse nature of the disturbances that might ensue, all waves have a similar behavior. The sound is a kind of wave that propagates only in the presence of a support means capable of the disturbance. The general concepts of waves used to describe the sound, but, conversely, sound phenomena can better understand some of the characteristics of wave behavior. domino players, such as additional entertainment, game tokens placed upright next to each other at a distance less than the length of the chips forming a row. When given a boost to the tab at one end of an action is a chain; each file transmitted to its neighbor the boost received which spreads from one extreme to another throughout the row. In physical terms one could say that a wave has spread through the dominoes. The idea of \u200b\u200bwave physics corresponds to a local disturbance of any kind that moves or propagates through a material medium or even in a vacuum. Some kinds of waves need to propagate the existence of a material means that, as the dominoes, then the backing of the disturbance, are generically called mechanical waves. The sound waves are formed in the surface water, waves in spring or ropes, are examples of mechanical waves and correspond to compression, deformation and, in general, environmental disturbances that propagate through it. However, there are waves that can get fresh even in the absence of material medium, ie in a vacuum. Are electromagnetic waves or electromagnetic fields travelers; to this second category are light waves. Regardless of this distinction, there are certain characteristics that are common to all waves, whatever their nature, and that together define the so-called wave behavior, ie a series of phenomena that distinguish the behavior typical behavior own corpuscles, or particles. wave motion The type of movement characteristic of waves is called wave motion. Its essential property is that it involves a mass transport from one point to another. Thus, there is a domino or a set of conditions moving forward from the starting point at the end, on the contrary, their individual movement does not reach more than an inch. The same happens in the wave that is generated on the surface of a lake or produced in a string by vibrating one end. In all cases the constituent particles of the medium move relatively little from its position equilibrium. What are advancing and progressing them, but the disturbance that passed each other. The wave motion is only a transport of energy and momentum. Types wave coupled to a first classification of mechanical and electromagnetic waves, it is possible to distinguish different types of waves in response to different criteria. In relation to the scope of wave propagation can be classified into one-dimensional : Those who, like waves on the docks or in the ropes, spread along one spatial direction. Dimensional: Propagate in any direction of a plane surface. Surface waves are also referred to as this group are the waves that occur on the surface of a lake when a stone is dropped on it. Given the frequency of local disturbance which they spring, waves are classified as: Periodicals: correspond to the propagation characteristics of periodic disturbances such as vibrations or oscillations that involve repetitive variations of some property. Thus, in a cord attached to one end of a vibrator spread of a periodic wave. Non-recurrent: The disruption that caused it occurs in isolation and in the case of repetition, successive shocks have different characteristics. Isolated waves, as in the case of dominoes, are also called pulses. Under the direction of propagation coincides or not with the direction in which the disturbance occurs, the waves can be: Longitudinal: The local environmental movement achieved by the disruption takes place in the forward direction of the wave. A spring that is compressed resulting in a longitudinal wave. Transverse : environmental disturbance occurs in the direction perpendicular to the propagation. In the waves produced on the surface of the water particles vibrate from top to bottom and vice versa, while the wave motion in the plane perpendicular progresses. The same is true in the case of a rope, each point vibrates vertically, but the disturbance moving in the direction of the horizontal line. Both are transverse waves. wave propagation The mechanism by which a one-dimensional mechanical wave propagates through a material medium can be described initially considering the case of waves on a spring. When the spring is compressed at one point and allowed to free the recuperative forces tend to restore the collapsed portion of the spring to equilibrium. But because different parts of the spring are held together by elastic forces, the dilation of a part will carry the compression of the next and so on until it reaches the far end. In ripples on the surface of a lake, the forces between water molecules maintain the free surface like a tense movie. These binding forces between the component particles are responsible for a perturbation at one point spread to the next, repeating the process again and again gradually in all directions from the surface of the liquid, resulting in forward motion of circular waves. As can be inferred from the propagation mechanism described, the properties of the medium strongly influence the characteristics of waves. Thus, the speed of a wave depend on the speed with which each particle of the medium is capable of transmitting the shock to his partner. The most rigid lead to higher speeds than the most flexible. In a spring of spring constant k low wave will spread more slowly than in another that has a higher k. The same applies to the most dense on the less dense. No media is perfectly elastic material. The particles that form a greater or lesser extent rub together, so that part of the energy transferred from one to another is dissipated as heat. This energy loss results, as in the case of vibration, attenuation or damping. However, the study of waves in the simplest terms without these undesirable effects of friction. Magnitudes characteristics of wave motion A harmonic wave is produced by the propagation of a simple harmonic vibration. Each point of the medium is achieved by the disturbance describes a simple harmonic motion that goes from one particle to another. While the starting point or focus that keep vibration causes movement, the different particles of the medium are oscillating around their equilibrium positions, constituting together a series of harmonic oscillators whose vibrations are so much delayed or out of step on the focus, the greater the distance it, or what is the same, the longer it takes for the disturbance to reach them. features simple harmonic vibration (MAS) in a middle point also defines the relevant characteristics of the wave at that point. Thus the state of vibration or disturbance of the medium is determined by the elongation, the period T of the wave coincides with the period of MAS that spreads, ie the time used any of the particles of the medium to carry out one complete oscillation, frequency faiths the inverse of the period f = 1 IT and accounts number of oscillations per second. The amplitude A represents the maximum displacement experienced by a particle of the medium with respect to its equilibrium position. The harmonic wave propagation in a string gives rise to a sine wave that moves along it. Unlike MAS wave motion spreads and progresses through the media. This allows to introduce a new characteristic quantity that is unique to this type of movement and is called wavelength. If at a given time is take out a photograph of the string looks like this is spread by a harmonic wave, the result would be a line that constitutes the sine wave profile at that time. Another photograph taken in a later show that the sinusoid has advanced. In any case, the length of the rope taken with its sign (height of waves in this type measures the magnitude or the state of disturbance) is repeated at equal intervals of distance, each of which is a length wave. The wavelength is thus the distance between two successive points of the medium are in the same state of shock. Coincides with the space that runs along the wave during a time interval equal to one period, ie space = speed x time λ = v. T (13.1) where v is the velocity, assumed constant progress of the disturbance. Expressed in terms of frequency, the above equation becomes: λ = v / f (13.2) and indicates that the wavelength λ and frequency f are two quantities are inversely proportional, so that the higher is the less the other. WAVE EQUATION The wave motion can be expressed in mathematical form by an equation that describes a vibration moving through a medium. This requires from the equation defining the oscillation of outbreak or origin of the disturbance. If simple harmonic motion is the equation for is: Y = A. sin ω t Y = A. sen (2.π.ft) Where elongation is represented, in this case, the letter Y, as in transverse waves, as in the strings, equivalent to a height. As the disturbance moves at a speed v, at a distance r will require some time: t '= r / v That means that the state of disturbance of any point P located at a distance r from the focus O coincides with the focus had t 'seconds earlier. This is a time delay indicates how much disruption is delayed when arriving at P with respect to the focus. Therefore, if the elongation equation that describes the state of focus is changed by tt t 'is obtained an equation that describes the state of disturbance of point P: A.sen Y = ω ( t - r / v) tyr Since referring to moments and distances generic generic focus on O, the above equation describes the state of disturbance environment, measured by the height Y at any point and at any time, which is a good mathematical description of a harmonic wave. The argument for the sine function can also be expressed in the form ω . (T - r / v) = (2.π / T). [T - r / (λ / T)] = 2.π ( t / T - r / λ) as ω = 2 π / T v = λ / T, which allows you to write the wave equation in terms of its parameters or constant characteristics such as amplitude A, the period T and the length λ. A.sen 2.π Y = (t / T - r / λ) Equation wave is also called the wave function and may refer to a generic perturbation which does not consist precisely in point, if Y is replaced by the Greek letter Ψque defines the magnitude of the disturbance. In this case, the wave function takes the form Ψ = A.sen 2.π (t / T - r / λ) where Ψpuede represent alteration, over time, as different physical properties as density, pressure, electric field or magnetic field, for example, and its spread throughout the space.
Moments like those
If a single pendulum (l 
