In everyday life, a person constantly encounters manifestations of oscillatory motion. This is the swing of the pendulum in the clock, the vibrations of automobile springs and the entire car. Even an earthquake is nothing but vibrations of the earth's crust. High-rise buildings also sway 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 wall clock pendulum. The passage of the pendulum from the highest point on the left to the highest point on the right is called its full swing. The period of one such complete oscillation is called the perimeter. The oscillation frequency is the number of oscillations per second.
To study oscillations, a simple thread 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 at absoluteflexibility and lack of friction, you get a theoretical, so-called mathematical pendulum.
The oscillation period of such an "ideal" pendulum can be calculated using the formula:
T=2π √ l / g, where l is the length of the pendulum, g is the free fall acceleration.
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.
Transformation of energy
What is the mechanism of pendulum movements, repeating with a certain period, even to infinity, if there were no friction and resistance forces, to overcome which a certain work is required?
The pendulum begins to oscillate due to the energy imparted to it. At the moment the pendulum is taken away from the vertical position, we give it a certain amount of potential energy. When the pendulum moves from the top point to the starting position, potential energy is converted into kinetic energy. In this case, the speed of the pendulum will become the greatest, since the force imparting acceleration decreases. Due to the fact that in the initial position the speed of the pendulum is the greatest, it does not stop, but by inertia moves further along the arc of a circle to exactly the same height as the one from which it descended. This is how energy is converted during oscillatory motion from potential to kinetic.
The height of the pendulum is equal to the height of its lowering. Galileo came to this conclusion while conducting an experiment with a pendulum, later named after him.
The swing of a pendulum is an indisputable example of the law of conservation of energy. And they are called harmonic vibrations.
Sine wave and phase
What is a harmonic oscillatory motion. To see the principle of such movement, you can conduct the following experiment. We hang a funnel with sand on the crossbar. Under it we put a sheet of paper, which can be shifted perpendicular to the fluctuations of the funnel. Having set the funnel in motion, we shift the paper.
The result is a wavy line written in sand - a sinusoid. These oscillations, occurring in accordance with the law of the sine, are called sinusoidal or harmonic. With such fluctuations, any quantity characterizing the movement will change according to the law of sine or cosine.
Having examined the sinusoid formed on the cardboard, it can be noted that sand is a layer of sand in its various sections of different thicknesses: at the top or trough of the sinusoid, it was most densely piled up. This suggests that at these points the pendulum's speed was the smallest, or rather zero, at those points where the pendulum reversed its motion.
The concept of phase plays a huge role in the study of oscillations. Translated into Russian, this word means "manifestation". In physics, a phase is a specific stage of a periodic process, that is, the place on the sinusoid where the pendulum is currently located.
Hesitations on the loose
If the oscillatory system is given movement and then stoppedthe influence of any forces and energies, 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 only variable (faster at the bottom and slower at the top), but also not uniformly variable.
In harmonic oscillations, the force that gives the pendulum acceleration becomes weaker with a decrease in the amount of deviation from the equilibrium point. There is a proportional relationship between force and deflection distance. Therefore, such vibrations are called harmonic, in which the angle of deviation from the equilibrium point does not exceed ten degrees.
Forced movement and resonance
For practical application in engineering, vibrations are not allowed to decay, imparting an external force to the oscillatory system. If the oscillatory movement occurs under external influence, it is called forced. Forced vibrations occur with the frequency that an external influence 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 coinciding, the amplitude of the oscillations increases. An example of such an increase is a swing that takes off higher if, during movement, you give them acceleration, hitting the beat of their own movement.
This phenomenon in physics is called resonance and is of great importance for practical applications. For example, when tuning a radio receiver to the desired wave, it is brought into resonance with the corresponding radio station. The phenomenon of resonance also has negative consequences,leading to the destruction of buildings and bridges.
Self-sufficient systems
Besides forced and free vibrations, there are also self-oscillations. They occur with the frequency of the oscillating system itself when exposed to a constant rather than a variable force. An example of self-oscillations is a clock, the movement of the pendulum in which is provided 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 impact 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 various and indispensable: from swing swings to the production of rocket engines.
