Name: resonance in driven oscillators
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 6 s
Channel: JoVE

Considere quatro pêndulos amarrados a uma corda e suspensos por um suporte rígido. Sejam os comprimentos dos pêndulos A e C idênticos, enquanto os pêndulos B e D têm comprimentos diferentes.
Quando o pêndulo A é deslocado, ele sofre oscilação livre com uma frequência natural. A frequência natural é a frequência na qual o pêndulo oscila naturalmente na ausência de qualquer amortecimento ou força motriz.
A energia do pêndulo A é transferida para os outros pêndulos, forçando-os a oscilar com uma frequência de condução. Essas oscilações resultantes devido à força motriz externa exercida pelo pêndulo A são conhecidas como oscilações forçadas.
A força motriz que atua nos pêndulos pode ser representada pela força que varia periodicamente com amplitude F0 e a frequência angular motriz.
Ao adicionar a força motriz obtida às equações de força do oscilador harmônico amortecido, a equação de movimento do oscilador forçado é obtida.

oscilações forçadas

Quando um oscilador é forçado com uma força motriz periódica, o movimento pode parecer caótico. Os movimentos de tais osciladores são conhecidos como transientes. Após os transientes desaparecerem, o oscilador alcança um estado estável, onde o movimento é periódico e o deslocamento é determinado.

<img alt="Equation1" src="/files/ftp_upload/12771/12771_Equation_1.png" style="text-align: center; height: 13px;" />

Utilizando as equações de força e movimento, obtém-se a amplitude do oscilador forçado. Ela depende da frequência natural e da frequência da força externa aplicada.

<img alt="Equation2" src="/files/ftp_upload/12771/12771_Equation_2.png" style="text-align: center; height: 40px;" />

Na equação para a amplitude, quando a frequência da força externa é muito menor (ou muito maior) do que a frequência natural, o quadrado da diferença das duas frequências angulares é positivo e grande, resultando em uma pequena amplitude para as oscilações da massa. Conforme a frequência da força externa se aproxima da frequência natural do sistema, a amplitude das oscilações aumenta. Quando a frequência da força externa é igual à frequência natural do sistema, isso resulta em amplitude máxima.

Vamos considerar um exemplo da vida real. A maioria de nós já brincou com brinquedos que envolvem um objeto suspenso em uma banda elástica, como uma bola de ping pong presa por uma corda. No início, quando o dedo é mantido parado, a bola salta para cima e para baixo com uma pequena quantidade de amortecimento. Se o dedo é movido para cima e para baixo lentamente, a bola acompanha sem pular muito. Conforme a frequência com que o dedo se move para cima e para baixo aumenta, a bola responde oscilando com aumento de amplitude. Quando a bola é forçada em sua frequência natural, as oscilações da bola aumentam de amplitude a cada oscilação enquanto é forçada.

O fenômeno de forçar um sistema com uma frequência igual à sua frequência natural é chamado de ressonância. Um sistema que está sendo forçado em sua frequência natural é considerado como estando em ressonância. Conforme a frequência de forçamento fica progressivamente maior do que a frequência ressonante ou natural, a amplitude das oscilações diminui até que as oscilações quase desapareçam e o dedo simplesmente se mova para cima e para baixo com pouco efeito na bola.

Este texto foi adaptado de <a href="https://openstax.org/books/college-physics/pages/16-8-forced-oscillations-and-resonance">Openstax, College Physics, Section 16.8: Forced Oscillations and Resonance </a> e <a href="https://openstax.org/books/university-physics-volume-1/pages/15-6-forced-oscillations">Openstax, University Physics Volume 1, Section 15.5: Forced Oscillations.</a>

Oscilações Forçadas

Quando um oscilador é forçado com uma força motriz periódica, o movimento pode parecer caótico. Os movimentos de tais osciladores são conhecidos como transientes. Depois...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Oscillations

Oscilações

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 driving frequency. If the driving frequency is much lower or much higher than the natural frequency, the difference between the two angular frequencies is large. In that case, the amplitude is small. As the driving frequency gets closer to the natural frequency, the amplitude increases. When the two frequencies are equal, the amplitude reaches its maximum.

A common example is a paddle ball suspended from a finger by an elastic band. When the finger stays still, the ball bounces up and down with only a small amount of damping. If the finger moves up and down slowly, the ball follows along and does not bounce much on its own. As the finger moves faster, the ball responds with larger oscillations.

When the ball is driven at its natural frequency, its motion grows with each oscillation for as long as the force continues. This is resonance. A system driven at its natural frequency is said to resonate. If the driving frequency becomes higher than the resonant or natural frequency, the amplitude drops again. The oscillations then nearly disappear, and the finger moves up and down with little effect on the ball.

Resonance in Driven Oscillators

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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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Simple Harmonic Motion from Circular Motion

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Energy Conservation in Simple Harmonic Motion

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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...

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key terms and concepts

See how driven oscillators reach steady motion, why amplitude depends on driving and natural frequency, and how resonance makes a paddle ball swing higher.

Resonance in Driven Oscillators | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

Resonance in Driven Oscillators

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