In everyday life, a person constantly encounters manifestations of oscillatory motion. This is the swing of the pendulum in hours, the fluctuations of car springs and the whole car. Even an earthquake is nothing but the vibrations of the earth's crust. Tall buildings also hesitate from strong gusts of wind. Let's try to figure out how physics explains this phenomenon.
Pendulum as an oscillatory system
The most obvious example of oscillatory motion is the pendulum of a wall clock. The passage of the pendulum from the highest point on the left to the highest point on the right is called its complete oscillation. The period of one such complete oscillation is called the perimeter. The oscillation frequency is the number of oscillations per second.
To study the oscillations, a simple filament pendulum is used, which is made by hanging a small metal ball on a thread. If we imagine that the ball is a material point, and the thread has no mass with absolute flexibility and the absence of friction, we get a theoretical, so-called mathematical pendulum.
The oscillation period of such an βidealβ pendulum can be calculated by the formula:
T = 2Ο β l / g,
where l is the length of the pendulum, g is the acceleration of gravity.
The formula shows that the period of oscillation of the pendulum does not depend on its mass and does not take into account the angle of deviation from the equilibrium position.
Energy conversion
What is the mechanism of the pendulum's movements, repeating with a certain period, even to infinity, if there were no friction and resistance forces, to overcome which some work is required?
The pendulum begins to oscillate due to the energy communicated to it. At the moment the pendulum is diverted from a vertical position, we inform it of a certain supply of potential energy. When the pendulum moves from the top point to its original position, the potential energy goes into kinetic. In this case, the speed of the pendulum will become the greatest, since the force imparting acceleration decreases. Due to the fact that the pendulum has the highest speed in the initial position, it does not stop, but by inertia it moves further along the arc of a circle to exactly the same height as that with which it fell. This is how energy is converted during vibrational motion from potential to kinetic.
The height of the pendulum is equal to the height of its lowering. This conclusion was reached by Galileo, conducting an experiment with a pendulum, later named after him.
The oscillations of the pendulum are an undeniable example of the law of conservation of energy. And they are called harmonic vibrations.
Sine wave and phase
What is harmonic oscillatory motion? To see the principle of such a movement, one can conduct the following experiment. We hang a funnel with sand on the crossbar. Under it we put a sheet of paper that can be shifted perpendicular to the vibrations of the funnel. Putting the funnel in motion, we shift the paper.
The result is a wave-like line written in sand - a sinusoid. Such oscillations occurring in accordance with the law of sinus are called sinusoidal or harmonic. With such oscillations, any value characterizing the motion will change according to the law of sine or cosine.
Having examined the sinusoid formed on the cardboard, it can be noted that the sand is a layer of sand in its various sections of different thicknesses: it poured most densely on the top or bottom of the sinusoid. This suggests that at these points the speed of the pendulum was the smallest, or rather zero, at those points where the pendulum reversed the movement.
The concept of phase plays a huge role in the study of oscillations. Translated into Russian, this word means "manifestation." In physics, the phase is the specific stage of a periodic process, that is, the place on the sinusoid where the pendulum is currently located.
Fluctuations on the loose
If the oscillatory system is given movement, and then the influence of all forces and energies is stopped, then the oscillations of such a system will be called free. The oscillations of the pendulum, which is left to itself, will gradually begin to fade, the amplitude will decrease. The movement of the pendulum is not just variable (faster at the bottom and slower at the top), but also the variable is not uniform.
In harmonic oscillations, the force giving the pendulum acceleration becomes weaker with a decrease in the deviation from the equilibrium point. There is a proportional relationship between force and deflection distance. Therefore, harmonic vibrations are called those in which the angle of deviation from the equilibrium point does not exceed ten degrees.
Forced Movement and Resonance
For practical use in technology, the oscillations are not allowed to decay, imparting external force to the oscillating system. If the oscillatory movement occurs under external influence, it is called forced. Forced vibrations occur with the frequency that the external action sets them. The frequency of the acting external force may or may not coincide with the frequency of the natural oscillations of the pendulum. When coincident, the amplitude of the oscillations increases. An example of such an increase is the swing, which soars higher if you give them acceleration while moving, falling in time with their own movement.
This phenomenon in physics is called resonance and is of great importance for practical application. For example, when tuning the radio to the desired wave, it is brought into resonance with the corresponding radio station. The resonance phenomenon has negative consequences, leading to the destruction of buildings and bridges.
Self-contained systems
In addition to forced and free oscillations, there are also self-oscillations. They occur with the frequency of the oscillating system itself when it is exposed to a constant rather than a variable force. An example of a self-oscillation is a clock in which the movement of the pendulum is ensured and maintained by unwinding the spring or lowering the load. When playing the violin, the natural vibrations of the strings coincide with the force arising from the action of the bow, and a sound of a certain tonality appears.
Oscillatory systems are diverse, and the study of the processes occurring in them in practical experiments is interesting and informative. The practical application of oscillatory motion in everyday life, science and technology is different and irreplaceable: from rocking swings to the production of rocket engines.