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

물 표면에 떠 있는 통나무를 생각해 보십시오. 아래로 밀고 위아래로 흔들리게 되면 평균 위치를 중심으로 진동합니다. 시간이 지남에 따라 소산력은 진동의 진폭을 감소시키며 감쇠 고조파 운동 방정식으로 설명할 수 있습니다.
해결 시 허수 부분이 0이 아닌 경우 시간 종속 지수 감쇠 엔벨로프 내의 위치 및 각도 주파수에 상대적인 미분 방정식에 대한 일반 솔루션이 얻어집니다.
각 주파수에 따라 시스템은 다양한 유형의 댐핑 조건을 나타냅니다. 감쇠력이 낮으면 각 주파수는 고유 주파수와 유사합니다. 따라서 언더댐핑 조건에서 시스템은 몇 가지 가능한 사이클을 만든 후 감쇠 진폭으로 진동합니다.
임계 댐핑 조건에서는 댐핑력과 복원력이 동일하고 각 주파수가 0이 되어 시스템 진동이 기하급수적으로 페이드 아웃됩니다.
반면에 과감쇠 상태에서는 감쇠력이 상대적으로 커서 시스템이 천천히 평형에 도달합니다.

댐핑의 종류

시스템의 감쇠량이 점진적으로 증가하면 감쇠가 반대되어 앞뒤 운동이 느려지기 때문에 주기와 주파수가 영향을 받기 시작합니다(순 힘은 두 방향 모두에서 더 작음). 매우 큰 양의 감쇠가 있는 경우 시스템은 진동하지도 않습니다. 대신 천천히 균형을 향해 움직입니다. 간단히 말해서, 과도한 감쇠 시스템은 평형을 향해 천천히 이동하는 반면, 감쇠가 부족한 시스템은 평형을 향해 빠르게 이동하지만 평형점을 중심으로 진동합니다. 대조적으로, 임계 감쇠 시스템은 평형점을 중심으로 진동하지 않고 평형을 향해 최대한 빠르게 이동합니다.

일반적으로 임계 감쇠는 이러한 시스템이 빠르게 평형으로 돌아올 뿐만 아니라 평형 상태를 유지하기 때문에 종종 필요합니다. 또한, 임계 감쇠 시스템에 일정한 힘이 가해지면 오버슈팅이나 새 위치에 대한 진동 없이 시스템이 가능한 가장 짧은 시간에 새로운 평형 위치로 이동합니다. 예를 들어, 바늘 게이지가 있는 욕실 저울 위에 사람이 서 있으면 바늘이 진동하지 않고 평형 위치로 이동합니다. 바늘이 안정되기 전에 오랜 시간 동안 새로운 평형 위치를 중심으로 진동한다면 매우 불편할 것입니다. 감쇠력은 성격에 따라 크게 달라질 수 있습니다. 예를 들어 마찰은 때때로 속도와 무관합니다. 그러나 많은 감쇠력은 속도에 따라 달라지며 때로는 복잡한 방식으로, 때로는 단순히 속도에 비례하기도 합니다.

이 텍스트는 <a href="https://openstax.org/books/college-physics/pages/16-7-damped-harmonic-motion">에서 발췌되었습니다. Openstax, 대학 물리학, 섹션 16.7: 감쇠된 조화 운동 </a>및 <a href="https://openstax.org/books/university-physics-volume-1/ 페이지/15-5-damped-oscillations">Openstax, 대학 물리학 1권, 섹션 15.4: 감쇠 진동.</a>

시스템의 댐핑량이 점차적으로 증가하면 댐핑이 반대되기 때문에 기간과 주파수가 영향을 받기 시작하여 속도가 느려집니다.

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Oscillations

진동

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

How Damping Changes Oscillations

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