Name: how damping changes oscillations
Uploaded: 2023-04-30T11:09:03.000Z
Duration: 1 min 20 s
Channel: JoVE

Considere un tronco de madera flotando en la superficie del agua. Cuando se empuja hacia abajo y se le permite balancearse hacia arriba y hacia abajo, oscila alrededor de su posición media. Con el tiempo, la fuerza disipativa reduce la amplitud de la oscilación, y se puede describir mediante la ecuación del movimiento armónico amortiguado.
Al resolver, si la parte imaginaria es distinta de cero, se obtiene la solución general de la ecuación diferencial relativa a la posición y la frecuencia angular dentro de la envolvente de decaimiento exponencial dependiente del tiempo.
Dependiendo de la frecuencia angular, el sistema exhibe diferentes tipos de condiciones de amortiguación. Cuando la fuerza de amortiguación es baja, la frecuencia angular se asemeja a la frecuencia natural. Por lo tanto, en condiciones de poca amortiguación, el sistema oscila con amplitud decreciente después de hacer algunos ciclos posibles.
En condiciones críticas de amortiguación, las fuerzas de amortiguación y restauración son iguales y la frecuencia angular se vuelve cero, lo que hace que las oscilaciones del sistema se desvanezcan exponencialmente.
Por otro lado, en condiciones de sobreamortiguación, la fuerza de amortiguación es relativamente grande, lo que hace que el sistema alcance lentamente el equilibrio.

tipos de amortiguamiento

Si la magnitud de amortiguamiento en un sistema aumenta gradualmente, el periodo y la frecuencia comienzan a verse afectados porque el amortiguamiento se opone y, por lo tanto, el movimiento de ida y vuelta es más lento (la fuerza neta es menor en ambas direcciones). Si hay una gran magnitud de amortiguamiento, el sistema ni siquiera oscila; en cambio, se mueve lentamente hacia el equilibrio. En resumen, un sistema sobreamortiguado se mueve lentamente hacia el equilibrio, mientras que un sistema subamortiguado se mueve rápidamente hacia el equilibrio, pero oscilará alrededor del punto de equilibrio mientras lo hace. En contraste, un sistema críticamente amortiguado se mueve tan rápido como sea posible hacia el equilibrio sin oscilar alrededor del punto de equilibrio. En general, el amortiguamiento crítico a menudo es deseado porque dicho sistema no solo regresa rápidamente al equilibrio, sino que también se mantiene en equilibrio. Además, una fuerza constante aplicada a un sistema críticamente amortiguado mueve el sistema a una nueva posición de equilibrio en el menor tiempo posible, sin sobrepasar ni oscilar alrededor de la nueva posición. Por ejemplo, cuando una persona se para sobre una báscula de baño que tiene una aguja indicadora, la aguja se mueve a su posición de equilibrio sin oscilar. Sería bastante incómodo si la aguja oscilara alrededor de la nueva posición de equilibrio durante mucho tiempo antes de estabilizarse. Las fuerzas de amortiguamiento pueden variar mucho en carácter. La fricción, por ejemplo, a veces es independiente de la velocidad. Sin embargo, muchas fuerzas de amortiguamiento dependen de la velocidad, a veces de formas complejas y a veces simplemente siendo proporcionales a la velocidad. Este texto está adaptado de <a href="https://openstax.org/books/college-physics/pages/16-7-damped-harmonic-motion">Openstax, College Physics, sección 16.7: Movimiento Armónico Amortiguado </a>y <a href="https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations">Openstax, University Physics Volume 1, sección 15.4: Oscilaciones Amortiguadas.</a>

Tipos de Amortiguamiento

Si la cantidad de amortiguación en un sistema se incrementa gradualmente, el período y la frecuencia comienzan a verse afectados porque la amortiguación se opone y, por lo tanto, se ralentiza ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Oscillations

Oscilaciones

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Types of Damping

how damping changes oscillations

Damping changes how a system oscillates by reducing its back-and-forth motion. As damping increases, the period and frequency begin to change because damping opposes motion and lowers the net force in both directions.

When damping is very large, the system stops oscillating altogether. It then moves slowly toward equilibrium. An overdamped system reaches equilibrium slowly. An underdamped system reaches equilibrium faster, but it oscillates around the equilibrium point while doing so.

A critically damped system is different. It moves to equilibrium as quickly as possible without overshooting or oscillating. This is often the desired behavior because the system returns to equilibrium rapidly and stays there.

Critical damping is also useful when a constant force creates a new equilibrium position. In that case, the system moves to the new position in the shortest time possible without overshooting. A bathroom scale with a needle gauge is a common example. The needle moves to its equilibrium position and does not keep bouncing around it, which would be inconvenient.

Damping forces can also have different forms. Friction is sometimes independent of velocity. In many other cases, damping depends on velocity, either in complex ways or simply in proportion to velocity.

How Damping Changes Oscillations

simple harmonic motion

Period and Frequency in Simple Harmonic Motion

Simple harmonic motion describes oscillatory motion when the net force follows Hooke's law. In this type of motion, the force acts toward the equilibrium position. If there is no damping from friction or other non-conservative forces, the oscillator moves with equal displacement on both sides of equilibrium. The period of a simple harmonic oscillator is found from the equation of motion. Period is the time for one complete oscillation. Frequency is the inverse of period, so the two values can...

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characteristics of simple harmonic motion

characteristics-of-simple-harmonic-motion

Simple Harmonic Motion: Period and Phase

Simple harmonic motion depends on how displacement, force, and acceleration work together. In this motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and points in the opposite direction. That restoring force pulls the object back toward equilibrium. The period and frequency of a simple harmonic oscillator do not depend on amplitude. A diving board shows this idea well. A stiff, thick diving board has a large force constant, so it has a...

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oscillations about an equilibrium position

oscillations-about-an-equilibrium-position

Stable Equilibrium and Atomic Oscillation

Stable equilibrium is a key idea in oscillation. When an object sits at a stable equilibrium point, a small push moves it away, but it then tends to oscillate around that point. If the equilibrium point is unstable, a slight disturbance will not bring the object back. The transcript also describes a half-stable equilibrium point. It is still considered unstable, but the name comes from the fact that the force on only one side points toward the equilibrium point. That makes it different from a...

energy in simple harmonic motion

Simple Harmonic Motion: Energy and Speed

Simple harmonic motion combines potential energy and kinetic energy. In a spring-like oscillator, Hooke’s law explains the potential energy stored when the string or spring is stretched or compressed. Because there are no dissipative forces, the object also has kinetic energy as it moves.

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frequency of spring-mass system

How Mass and Spring Stiffness Set Oscillation

A spring-mass system shows simple harmonic motion, and its oscillation rate depends on the mass and the spring force constant. In this model, the angular frequency, period, and frequency are set by those two values. They do not depend on the motion’s amplitude or on the initial conditions. To find these relationships, the system can be analyzed with Newton’s second law. Imagine a block on a spring on a frictionless surface. Three forces act on the mass: weight, the normal force, and the spring...

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simple harmonic motion and uniform circular motion

simple-harmonic-motion-and-uniform-circular-motion

Simple Harmonic Motion from Circular Motion

Simple harmonic motion and uniform circular motion are closely linked. Simple harmonic motion is oscillatory motion in a system where the net force follows Hooke’s law. Uniform circular motion is motion along a circular path at constant speed. A simple way to create simple harmonic motion is to use uniform circular motion. One example is a ball attached to a vertical turntable that spins at a steady rate. If you watch the ball’s shadow on the floor, the shadow, or projection, moves in simple...

problem solving: energy in simple harmonic motion

problem-solving-energy-in-simple-harmonic-motion

Energy Conservation in Simple Harmonic Motion

Energy conservation in simple harmonic motion explains how a spring and mass system shares energy as it moves back and forth around equilibrium. Simple harmonic motion, or SHM, is periodic motion in time and position. The object oscillates with a constant amplitude and frequency. In SHM, kinetic energy and potential energy change into each other continuously. A good example is the spring in a car shock absorber as the car moves on a bumpy road. The wheel attached to the spring oscillates in...

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simple pendulum

Pendulum Motion and Period

A simple pendulum is a small ball, or bob, hanging from a string that has negligible mass and does not stretch. Pendulums appear in everyday life, including clocks, swing sets, and a sinker on a fishing line. Their motion is a useful model for studying repeating movement. The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period does not depend on the bob’s mass or on the maximum displacement. For small angles, the pendulum behaves like...

torsional pendulum

Angular Oscillation in a Torsion String

Angular oscillation in a torsion string is shown by a rigid body suspended from a string that twists as it moves. The twisting of the string provides the restoring force. The string is ideally massless, and in practice its mass is much smaller than the rigid body&amp;#39;s mass, so it is neglected. When the angular displacement is small, the motion can be modeled as linear angular oscillation. The amplitude is measured as an angle. In this system, the role of mass is played by the rigid...

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physical pendulum

Physical Pendulum Motion and Inertia

A physical pendulum is a rigid body that hangs from a fixed pivot point and swings when it is displaced. Its motion is similar to a simple pendulum. To describe that motion, physicists use the small-angle approximation, where sin θ ≈ θ. This approximation is valid up to about 14°. The period and angular frequency of a physical pendulum can be found by comparing it with a spring-mass system. The mass moment of inertia is the key quantity that describes how the body’s mass is spread around the...

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measuring acceleration due to gravity

Using Pendulums to Find Gravity

Pendulums can be used to measure the acceleration due to gravity. A simple pendulum is a point mass attached to a string. A physical pendulum is an object that swings in a similar way, but its mass is spread out, so it cannot be treated as a point mass on a string. A physical pendulum is described using rotational motion and moment of inertia. In both types of pendulum, gravity provides the restoring force that brings the object back toward the middle of its swing. For a simple pendulum,...

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damped oscillations

Energy Loss in Oscillations

Oscillations in the real world often lose energy as they move. A system that keeps the same amplitude without any loss is called undamped. That kind of motion is rare, because friction and other non-conservative forces usually reduce the motion over time. Common examples show this clearly. A guitar string stops vibrating a few seconds after it is plucked. A swing also needs a person to keep pushing it if the motion is to continue. In some devices, such as car shock absorbers, damping is useful...

types of damping

Damping changes how a system oscillates by reducing its back-and-forth motion. As damping increases, the period and frequency begin to change because damping opposes motion and lowers the net force in both directions. When damping is very large, the system stops oscillating altogether. It then moves slowly toward equilibrium. An overdamped system reaches equilibrium slowly. An underdamped system reaches equilibrium faster, but it oscillates around the equilibrium point while doing so. A...

forced oscillations

Resonance in Driven Oscillators

Resonance in driven oscillators describes how a periodic force changes an object’s motion. A driven oscillator may first move in a messy way. These early motions are called transients. After the transients die out, the oscillator reaches a steady state. In this state, the motion becomes periodic and the displacement is determined. The amplitude of a driven oscillator can be found from the equations for force and motion. That amplitude depends on the natural frequency of the system and the...

concept of resonance and its characteristics

concept-of-resonance-and-its-characteristics

Resonance in Music, Cars, and Radios

Resonance is a key feature of driven oscillators, and it depends strongly on damping. Damping is the process that reduces motion by removing energy from the system. When a system must resonate at one specific frequency, very light damping is needed. Piano strings and many other musical instruments are common examples of this kind of response. Heavy damping works better when the goal is small-amplitude oscillations. A car suspension system uses this approach so that bumps do not produce large...

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key terms and concepts

Learn how damping affects oscillations, including underdamped, overdamped, and critically damped motion, plus why critical damping is often useful.

How Damping Changes Oscillations | JoVE K12

physics

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How Damping Changes Oscillations

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