Name: pendulum motion and period
Uploaded: 2023-04-30T11:08:39.000Z
Duration: 1 min 10 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

Energy

HS-PS3-5

Simple Pendulum

يعرف النموذج المثالي لكتلة نقطية معلقة من خيط غير مرن وعديم الكتلة باسم البندول البسيط.
ضع في اعتبارك قمة معلقة بحرية من سلسلة ثابتة إلى نقطة محورية. يتعرض لقوة الجاذبية وتوتر في السلسلة. في وضع التوازن ، توازن كلتا القوتين بعضهما البعض.
عندما يتم إزاحة الجزء العلوي من خلال إزاحة زاوية صغيرة ويتم تحريره ، فإنه يبدأ في التذبذب ذهابا وإيابا ، مما يؤدي إلى تنفيذ حركة توافقية بسيطة.
يتم حل قوة الجاذبية في موضع النازحة إلى قوى شعاعية وعرضية. المكون الشعاعي يقاوم التوتر في السلسلة. عزم الدوران القابل للاستعادة الذي يعمل في المستوى يساوي المكون العرضي مضروبا في طول الخيط ويعيد الجزء العلوي إلى وضع التوازن.
في البندول البسيط ، تتناسب قوة الاستعادة طرديا مع الإزاحة على طول القوس. من خلال تعديل معادلات الحركة التوافقية البسيطة ، يتم الحصول على فترة البندول البسيط.

البندول بسيط

<div style="direction:rtl">يتكون البندول البسيط من كرة صغيرة القطر معلقة بخيط، لها كتلة ضئيلة ولكنها قوية بما يكفي لعدم التمدد. في حياتنا اليومية، للبندول العديد من الاستخدامات، كما هو الحال في الساعات، وفي الأرجوحة، وفي ثقالة خط الصيد.  يعتمد الزمن الدوري للبندول البسيط على عاملين: طوله وتسارع الجاذبية. وهذه الدورة مستقلة تمامًا عن أي عوامل أخرى، مثل الكتلة أو الإزاحة القصوى. بالنسبة للإزاحات الصغيرة، يكون البندول مطابقًا للمذبذب التوافقي البسيط، وتكون فترة البندول مستقلة تقريبًا عن السعة، خاصة إذا كان θ أقل من 15° تقريبًا. وبتطبيق قانون نيوتن الثاني لأنظمة الدوران، يتم الحصول على معادلة حركة البندول. <img alt="الشكل1" src="/files/ftp_upload/12767/12767_ Equation_1.png" style="text-align: center; height: 35px;"> على سبيل المثال، فكر في بندولين بسيطين معلقين من أسلاك صغيرة مثبتة في سقف الغرفة. يرتفع كل بندول بمقدار 2 سم فوق الأرض. البندول 1 له كتلة كتلتها 10 كجم. البندول 2 له كتلة كتلتها 100 كجم. صف كيف ستختلف حركة البندول إذا تمت إزاحة البندول بمقدار 12°. بما أن كتلة الجسم ليس لها أي تأثير على حركة البندول البسيط، فإن حركة البندول لن تختلف على الإطلاق. تتأثر حركة البندول فقط بالدورة (المرتبطة بطول البندول) وبتسارع الجاذبية. هذا النص مقتبس من <a href="https://openstax.org/books/college-physics/pages/16-4-the-simple-pendulum">أوبنستاكس، الفيزياء الجامعية، القسم 16.4: البندول البسيط </a>و <a href="https://openstax.org/books/university-physics-volume-1/pages/15-4-pendulums">أوبنستاكس، الفيزياء الجامعية المجلد الأول، القسم 15.4: البندول</a>.</div>

يتكون البندول البسيط من كرة ذات قطر صغير معلقة من خيط ، لها كتلة ضئيلة ولكنها قوية بما يكفي لعدم التمدد. في يومنا اليومي ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Oscillations

تذبذبات

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 a simple harmonic oscillator. Its period is nearly independent of amplitude when the angle is less than about 15°.

Newton’s second law for rotational systems can be applied to a pendulum to find its equation of motion. This helps describe how the pendulum swings back and forth. For example, two pendulums can have very different bob masses, such as 10 kg and 100 kg, yet still move the same way if they have the same length and are displaced by the same angle.

If both bobs are pulled aside by 12°, their motion will not differ because mass does not affect the motion of a simple pendulum. The swing is set by the period, which is linked to the pendulum’s length, and by gravity. That is why two pendulums with different masses can still stay in step.

Pendulum Motion and Period

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: 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.

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

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

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...

/files/media/science-education/science-education-thumbs/12772.jpg

key terms and concepts

Explore how a simple pendulum moves, what sets its period, and why mass does not change its motion. Built for high school physics learners.

Pendulum Motion and Period | 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.

Florida Department of Education

SC.912.P.10

SC.912.P.10.6

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.A

Chemistry and Physics

IPC.6

IPC.6.C

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

Types of Potential Energy

Potential energy is also known as energy at rest or stored energy. Common types of potential energy include the gravitational potential energy stored in ...

Types of Kinetic Energy

The amount of kinetic energy of an object depends on its mass and speed. Consider two balls of different masses rolling down an inclined plane at the same ...

Kinetic Energy - I

It&#8217;s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the ...

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Potential Energy due to Gravitation

Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it ...

Energy in Simple Harmonic Motion

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

Simple harmonic motion (SHM) is a type of periodic motion in time and position, in which an object oscillates back and forth around an equilibrium ...

Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Molecular Kinetic Energy

The word &#34;gas&#34;&#160;comes from the Flemish word meaning &#34;chaos,&#34; first used to describe vapors by the chemist J. B. van Helmont. Consider ...

Electric Potential Energy

When an electric field accelerates a free positive charge q, it is given kinetic energy. The process is analogous to an object accelerated by a ...

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Enthalpy

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum ...

Energy In A Magnetic Field

If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this ...

using-differential-scanning-calorimetry-to-measure-changes-in-enthalpy

Using Differential Scanning Calorimetry to Measure Changes in Enthalpy

Source: Laboratory of Dr. Terry Tritt &#8212; Clemson University
Differential Scanning Calorimetry (DSC) is a method of thermodynamic analysis based on ...

Hess's Law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally ...

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the ...

Work-energy Theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

/files/media/science-education/science-education-thumbs/14702.jpg

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Energy and Work

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

conservation-of-energy-approach-to-system-analysis

Conservation of Energy Approach to System Analysis

Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI
The purpose of ...

Hooke's Law and Simple Harmonic Motion

energy-associated-with-a-charge-distribution

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a ...

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. [Clarification Statement: Emphasis is on explaining the meaning of mathematical expressions used in the model.] [Assessment Boundary: Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields.]

HS-PS3-1

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 ...

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium&#39;s ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

electric-potential-energy-in-a-uniform-electric-field

Electric Potential Energy in a Uniform Electric Field

When an electric field accelerates a free positive charge, it acquires kinetic energy. This process is analogous to an object being accelerated by a ...

Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motion of particles (objects) and energy associated with the relative position of particles (objects). [Clarification 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.]

HS-PS3-2

What is Energy?

The universe is composed of matter in different forms, and all forms of matter contain energy. &#xA0;The different forms of energy on Earth originate from ...

Chemical Reactions

A chemical reaction is a process by which the bonds in the atoms of substances are rearranged to generate new substances. Matter cannot be created or ...

Energy Transfer in Chemical Reactions

Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ...

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (&#x394;S&#xB0;rxn) can be calculated from the difference in standard ...

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy ...

Effects of Temperature on Free Energy

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or ...

Calculating Standard Free Energy Changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. ...

free-energy-changes-for-nonstandard-states

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; ...

Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for &#x394;G represents a driving force for the ...

gibbs-free-energy-and-thermodynamic-favorability

Gibbs Free Energy and Thermodynamic Favorability

Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. [Clarification 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 Boundary: Assessment for quantitative evaluations is limited to total output for a given input. Assessment is limited to devices constructed with materials provided to students.]

HS-PS3-3

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature ...

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the ...

conduction-convection-and-radiation-problem-solving

Conduction, Convection and Radiation: Problem Solving

There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting ...

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). [Clarification 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 Boundary: Assessment is limited to investigations based on materials and tools provided to students.]

HS-PS3-4

Pendulum Motion and Period

Description

Transcript

More videos by Standards