Name: simple harmonic motion: energy and speed
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 23 s
Channel: JoVE
Description: 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.

K12 Standards

Pennsylvania State Academic Standards

9-12

Physical Science

Energy

3.2.9-12.P

Energy in Simple Harmonic Motion

평형 상태에서 마찰이 없는 표면에서 힘 상수 k를 가진 스프링에 부착된 질량 m 블록을 고려하십시오.
블록이 변위될 때 초기 위치에서 최종 위치까지 변위를 따라 스프링의 힘에 의해 수행되는 작업은 변위에 비해 스프링에 저장된 위치 에너지의 양과 같습니다. 이것을 탄성 위치 에너지라고 합니다.
해제되면 블록은 간단한 조화 운동을 겪습니다. 앞뒤로 움직이는 데 필요한 에너지를 평행 이동 운동 에너지라고 하며 속도와 질량의 제곱에 정비례합니다.
진동하는 동안 두 에너지는 지속적으로 상호 작용하며 정현파 파형으로 표시됩니다. 탄성 위치 에너지는 최대 변위에서 최대이고 평행 운동 에너지는 평형 위치에서 최대입니다.
다른 위치에서 블록은 서로 다른 운동 및 위치 에너지 값을 가지며 그 합은 시스템의 총 에너지와 같습니다.
따라서 시스템의 총 에너지는 평행 이동 운동 에너지와 탄성 위치 에너지 사이에서 진동하기 때문에 일정하고 보존된 상태로 유지됩니다.

<ol>
	<li>오픈스택스. (2020). 대학 물리학 [웹 버전]. (페이지 번호 680-682) <a href="https://openstax.org/details/books/college-physics">https://openstax.org/details/books/college-physics</a></li>
</ol>

단순 조화 운동의 에너지

단조파 진동자의 에너지를 결정하려면 단조파 운동 중에 가질 수 있는 모든 형태의 에너지를 고려하십시오. 훅의 법칙에 따르면 단조파 진동자에서 줄이 압축/늘어지는 동안 저장된 에너지는 위치 에너지입니다. 단순고조파진동자는 소산력이 없기 때문에 운동에너지도 가지고 있다. 보존력이 존재하는 경우 진동 중에 두 에너지가 상호 변환될 수 있지만 총 에너지는 일정하게 유지됩니다. 단순 고조파 발진기의 총 에너지는 위치 에너지와 운동 에너지의 합과 같고 진폭의 제곱에 비례합니다. 다음과 같은 형태로 표현될 수 있습니다:

<img alt="Equation1" src="/files/ftp_upload/12765/12765_Equation_1.svg" style="text-align: center; height: 35px;" />

단조파 운동의 속도 크기는 전체 에너지 방정식을 재배열하고 풀어서 구합니다.

<img alt="Equation2" src="/files/ftp_upload/12765/12765_Equation_2.svg" style="text-align: center; height: 42px;" />

이 표현식을 대수적으로 조작하면 다음이 제공됩니다.

<img alt="Equation3" src="/files/ftp_upload/12765/12765_Equation_3.svg" style="text-align: center; height: 50px;" />

어디

<img alt="Equation4" src="/files/ftp_upload/12765/12765_Equation_4.svg" style="text-align: center; height: 42px;" />

최대 속도는 세 가지 요소에 따라 달라지며 진폭에 비례합니다. 변위가 최대이면 속도도 최대가 됩니다. 또한 동일한 변위에 대해 더 큰 힘을 가하기 때문에 더 단단한 시스템의 경우 최대 속도가 더 큽니다. 이 관찰은 최대 속도에 대한 표현식에서 볼 수 있습니다. 최대 속도는 힘 상수의 제곱근에 비례합니다. 마지막으로, 최대 속도는 질량의 제곱근에 반비례하기 때문에 질량이 더 큰 물체의 경우 최대 속도는 더 작습니다.

단순 고조파 발진기의 에너지를 결정하려면 단순 고조파 운동 중에 가질 수 있는 모든 형태의 에너지를 고려하십시오. 에 따르면...

/files/media/science-education/science-education-thumbs/12765.jpg

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Oscillations

진동

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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.

Simple Harmonic Motion: Energy and Speed

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...

/files/media/science-education/science-education-thumbs/12762.jpg

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...

/files/media/science-education/science-education-thumbs/12763.jpg

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 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.

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...

/files/media/science-education/science-education-thumbs/14718.jpg

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...

/files/media/science-education/science-education-thumbs/14743.jpg

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...

/files/media/science-education/science-education-thumbs/12768.jpg

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...

/files/media/science-education/science-education-thumbs/14719.jpg

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,...

/files/media/science-education/science-education-thumbs/14720.jpg

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

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...

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 simple harmonic motion stores potential and kinetic energy, why total energy stays constant, and what controls maximum velocity.

Simple Harmonic Motion: Energy and Speed | 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.

3.2.9-12.Q

Louisiana Student Standards for Science

High School

HS-PS3-2

HS-PS3-3

Tennessee Academic Standards

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.2

Next Generation Science Standards

HS-PS3-1

HS-PS3-5

Florida Department of Education

SC.912.P.10

SC.912.P.10.6

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.A

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3.2.9-12.O

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Kinetic Energy - II

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Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Elastic Potential Energy

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is ...

To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to ...

Problem Solving: Energy in Simple Harmonic Motion

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Students who demonstrate understanding can develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects). Clarifying Statement: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations. Assessment Boundry: N/A

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Students who demonstrate understanding can design, build and refine a device that works within given constraints to convert one form of energy into another form of energy. Clarifying Statement: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. Assessment Boundry: Assessment for quantitative evaluations is limited to total output for a given input. Assessment is limited to devices constructed with materials provided to students.

Students who demonstrate understanding can plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). Clarifying Statement: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. Assessment Boundry: Assessment is limited to investigations based on materials and tools provided to students.

3.2.9-12.R

force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular ...

force-and-potential-energy-in-three-dimensions

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function ...

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the ...

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Students who demonstrate understanding can develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. Clarifying Statement: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other. Assessment Boundry: Assessment is limited to systems containing two objects.

3.2.9-12.S

Simple Harmonic Motion: Energy and Speed

Description

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