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Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Standing Waves01:17

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Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Buoyancy and Stability for Submerged and Floating Bodies01:11

Buoyancy and Stability for Submerged and Floating Bodies

In fluid mechanics, buoyancy and stability are key concepts for understanding the behavior of submerged and floating bodies. When a stationary body is fully or partially submerged in a fluid, the fluid exerts a force on the body known as the buoyant force. This force acts vertically upward through a point called the center of buoyancy, which is the center of the displaced fluid volume. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...

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Video Experimental Relacionado

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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Published on: March 3, 2017

La inestabilidad de ondulación de una burbuja en colapso.

da Silveira R1, Chaieb, Mahadevan

  • 1Department of Physics, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Science (New York, N.Y.)
|February 26, 2000
PubMed
Resumen

Las burbujas de aire que se elevan en líquidos viscosos crean cúpulas de estallido lento que se pliegan en patrones ondulados. Este fenómeno geométrico, impulsado por la gravedad y las fuerzas de flexión, predice un número específico de ondas, confirmadas por experimentos.

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Área de la Ciencia:

  • Dinámica de fluidos La dinámica de fluidos.
  • Reología Reología.
  • Física de la superficie de las superficies.

Sus antecedentes:

  • Las burbujas en líquidos viscosos forman cúpulas superficiales.
  • A diferencia de las burbujas de jabón, estas cúpulas se derrumban lentamente bajo la gravedad.
  • Este colapso conduce a una estructura única ondulada o ondulada.

Objetivo del estudio:

  • Para investigar la física detrás del lento colapso y ondulación de las burbujas de aire en líquidos viscosos.
  • Formular un modelo teórico para el inicio y el crecimiento de las corrugadas superficiales.
  • Para establecer una relación cuantitativa entre las propiedades de las burbujas y la formación de ondas.

Principales métodos:

  • Modelado teórico de la dinámica de las capas de fluidos.
  • Análisis de la interacción entre las fuerzas gravitacionales y de flexión.
  • Observación experimental del comportamiento de las burbujas en fluidos viscosos.

Principales resultados:

  • Se desarrolló una teoría para el inicio de ondulaciones superficiales en láminas viscosas.
  • El crecimiento de las corrugadas se rige por un equilibrio de fuerzas gravitacionales y de flexión.
  • Se derivó una expresión cuantitativa para el número de ondas y se validó experimentalmente.

Conclusiones:

  • El efecto ondulante en las láminas de fluidos viscosos es principalmente un fenómeno geométrico.
  • La teoría derivada y la expresión de número de ondulación muestran una amplia aplicabilidad a través de varias propiedades de fluidos y escalas.
  • Los resultados experimentales apoyan fuertemente las predicciones teóricas para la formación de ondas.