Name: simple harmonic motion from circular motion
Uploaded: 2023-04-30T11:08:32.000Z
Duration: 1 min 42 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Earth and Environmental Science

Earth's Place in the Universe

ESS.EES.1.2

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

Simple Harmonic Motion and Uniform Circular Motion

חשבו על הירח במרחק A ממרכז כדור הארץ, מסתובב בתנועה מעגלית במהירות זוויתית קבועה.
הניחו למרכז כדור הארץ להיות המקור של מערכת קואורדינטות זמן התזוזה. כאשר הירח נע למיקום P, ההיטל שלו P' על ציר ה-x יוצר זווית Ф.
כאשר הירח נע רחוק יותר סביב כדור הארץ בכל זמן t, הוא יוצר זווית ωt+Ф. בהתבסס על היטל הירח על ציר x או y, מיקום ההיטל יכול להיות מסומן על ידי פונקציית קוסינוס או סינוס.
תקופת הירח יכולה להינתן על ידי היקף מסלול כדור הארץ על מהירותו. אם זוכרים את משוואת המהירות משימור אנרגיה ושינויה, נקבעת תקופת ההטלה של הירח.
מהירות הירח פועלת באופן משיק, בעוד שתאוצת הירח מכוונת רדיאלית פנימה.
רכיב ה-x של מהירות ותאוצת הירח שווה למהירות ולתאוצה של הקרנת הירח. סדרי הגודל שלהם מתקבלים על ידי היזכרות במשוואות המהירות והתאוצה.
כפי שנצפה, משוואות פרק הזמן, המיקום, המהירות והתאוצה של הקרנת הירח דומות לאלה של מתנד הרמוני פשוט.
לכן, הקרנה של תנועה מעגלית אחידה לאורך קוטר המעגל שבו מתרחשת התנועה המעגלית מייצגת תנועה הרמונית פשוטה.

תנועה הרמונית פשוטה ותנועה מעגלית אחידה

<div style="direction:rtl">

 למרות שתנועה הרמונית פשוטה ותנועה מעגלית אחידה עשויים להיות שני מושגים נפרדים, הם מתואמים ומתקשרים זה עם זה. תנועה הרמונית פשוטה היא תנועה תנודה במערכת שבה ניתן לתאר את הכוח הנקי על ידי חוק הוק, בעוד שתנועה מעגלית אחידה היא תנועה של עצם במסלול מעגלי במהירות קבועה.

 ישנה דרך קלה לייצר תנועה הרמונית פשוטה על ידי שימוש בתנועה מעגלית אחידה. לדוגמה, שקול כדור המחובר לפטיפון אנכי מסתובב אחיד, כשהצל שלו מוקרן על הרצפה. כאן, המיקום של הצל, המכונה גם הקרנה, מבצע תנועה הרמונית פשוטה. חוק הוק מתאר בדרך כלל תנועות מעגליות אחידות (⍵ קבוע) ולא מערכות בעלות תזוזות גדולות גלויות. לפיכך, התבוננות בהקרנה של תנועה מעגלית אחידה היא לרוב קלה יותר מאשר התבוננות במתנד הרמוני פשוט בקנה מידה גדול. 

 דוגמה נוספת היא נגן תקליטים שעובר תנועה מעגלית אחידה. חשוב על מוט דיבל המחובר בנקודה אחת בקצה החיצוני של פטיפון ועט המחובר לקצה השני של הדיבל. כשנגן התקליטים מסתובב, העט זז. אם נגרור פיסת נייר ארוכה מתחת לעט, התנועה שלו נתפסת כגל. מכאן ניתן להבין שהתנועה ההרמונית הפשוטה היא השלכה של תנועה מעגלית אחידה בקוטר של עיגול בו מתרחשת התנועה המעגלית. 

 טקסט זה מותאם מ <a href="https://openstax.org/books/college-physics/pages/16-6-uniform-circular-motion-and-simple-harmonic-motion">Openstax, College Physics, Section 16.6: Uniform Circular Motion and  Simple Harmonic Motion</a> and <a href="https://openstax.org/books/university-physics-volume-1/pages/15-3-comparing-simple-harmonic-motion-and-circular-motion">Openstax, University Physics Volume 1, Section 15.3: Comparing Simple Harmonic Motion and Circular Motion.</a>

 </div>

בעוד שתנועה הרמונית פשוטה ותנועה מעגלית אחידה עשויות להיות שני מושגים נפרדים, הן מתואמות ומתחברות זו לזו. הרמוני פשוט ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Oscillations

תנודות

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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 harmonic motion.

This link also helps explain why circular motion can be easier to study in some cases. Hooke’s law usually describes uniform circular motions with constant angular speed, rather than systems with large visible displacements. For that reason, the projection of uniform circular motion is often easier to observe than a precise large-scale simple harmonic oscillator.

A record player gives another clear example. A dowel rod is attached to one point on the outside edge of a turntable, and a pen is attached to the other end of the dowel. As the record player turns, the pen moves. If a long piece of paper is pulled under the pen, the motion is traced as a wave. This shows that simple harmonic motion can be seen as the projection of uniform circular motion along the diameter of the circle.

Simple Harmonic Motion from Circular Motion

simple-harmonic-motion-from-circular-motion

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 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...

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

key terms and concepts

Explore how uniform circular motion creates simple harmonic motion through projections, shadows, and a record player example for high school physics.

Simple Harmonic Motion from Circular Motion | 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

High School

Physical Science

SC.912.P.10

SC.912.P.10.6

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.A

Kepler's First Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. He ...

Kepler's Second Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His ...

Kepler's Third Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In ...

Detection of Black Holes

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their ...

Tidal Forces

The origin of Earth&#39;s ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be ...

circular-orbits-and-critical-velocity-for-satellites

Circular Orbits and Critical Velocity for Satellites

The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial ...

Gravity between Spherical Bodies

Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

Use models to illustrate the formation of the solar system.

ESS.EES.1.1

Uniform Circular Motion

Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller ...

Gyroscope: Precession

Precession can be demonstrated effectively through a spinning top. If a spinning top is placed on a flat surface near the surface of the Earth at a ...

While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic ...

Use mathematics and computational thinking to analyze Earth's motion through space.

Light as Energy

The energy required to carry out photosynthesis is light&#8212; typically electromagnetic radiation from the sun. The range of all possible wavelengths is ...

Nuclear Fusion

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process ...

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. This can be demonstrated within a classic food web ...

Energy Dynamics

The Food Chain
Energy is one of the most important abiotic factors in an ecosystem and organisms in an ecosystem are connected by the flow of energy and ...

Use models to illustrate how the sun produces energy.

ESS.EES.1.3

Radiation: Applications

The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives ...

What is Weather?

Overview

Weather refers to the current state of atmospheric conditions at a specific time and place. Weather is temporary and is influenced by the ...

What is Climate?

Climate refers to the prevailing weather conditions in a specific area over an extended period. As the saying goes, &#8220;Climate is what you expect. ...

Radiation Pressure: Problem Solving

The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface equals the energy density of the wave. The wave&#39;s momentum ...

Absorption of Radiation

The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:

where &#963; is the Stefan-Boltzmann constant, a ...

Construct an explanation to infer how incoming solar radiation interacts with Earth systems to support life.

ESS.EES.1.4

Explain how Earth's position relative to the sun influences conditions on Earth.

Simple Harmonic Motion from Circular Motion

Description

Transcript

More videos by Standards