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How Things Bounce: Energy, Force, and Speed in Simple Harmonic Motion!

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jackie

4/26/2023

AP Physics 1

AP Physics 1: Simple Harmonic Motion (SHM)

How Things Bounce: Energy, Force, and Speed in Simple Harmonic Motion!

Simple harmonic motion (SHM) is a fundamental physics concept describing repetitive oscillations through an equilibrium position, governed by restoring forces and energy conservation principles.

Conservation of energy in simple harmonic motion plays a crucial role in understanding oscillatory behavior, where mechanical energy switches between kinetic and potential forms.

• The frequency of object spring system in SHM depends on the spring constant and mass, following specific mathematical relationships.

Acceleration and force in simple harmonic motion are always directed toward the equilibrium position, with magnitude proportional to displacement.

• Understanding reference circles, pendulums, and damped oscillations provides practical applications of SHM principles.

...

4/26/2023

203

Simple Harmonic Motion: simplest version of periodic motion - repetitive motion back and forth through an equilibrium
if mass pulled beyond

View

Page 2: Energy Conservation and Oscillation Rates

The second page delves deeper into energy conservation principles and the mathematical relationships governing oscillation rates in SHM.

Definition: Total mechanical energy in SHM remains constant in the absence of friction, alternating between potential and kinetic energy.

Highlight: At maximum displacement, velocity is zero and all energy is potential; at equilibrium, velocity is maximum and all energy is kinetic.

Example: A rotating turntable demonstration shows how circular motion projects as simple harmonic motion, where the shadow of a rotating ball appears to move back and forth.

Vocabulary: Angular frequency ωω represents the rate of oscillation in radians per second, related to frequency by ω = 2πf.

Simple Harmonic Motion: simplest version of periodic motion - repetitive motion back and forth through an equilibrium
if mass pulled beyond

View

Page 3: Reference Circles and Pendulums

The final page explores the relationship between SHM and reference circles, along with practical applications in pendulum motion.

Definition: A reference circle provides a geometric interpretation of SHM, where the projection of uniform circular motion represents simple harmonic motion.

Example: A simple pendulum demonstrates SHM for small angles lessthan15°less than 15°, with its period depending only on length and gravitational acceleration.

Highlight: Real-world oscillations are typically damped due to friction, causing decreasing amplitude over time.

Quote: "Pendulum undergoes SHM for small angles where sin θ ≈ θ lessthan 15°less than ~15°"

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AP Physics 1

203

Apr 26, 2023

3 pages

How Things Bounce: Energy, Force, and Speed in Simple Harmonic Motion!

Simple harmonic motion (SHM) is a fundamental physics concept describing repetitive oscillations through an equilibrium position, governed by restoring forces and energy conservation principles.

Conservation of energy in simple harmonic motionplays a crucial role in understanding oscillatory behavior,... Show more

Simple Harmonic Motion: simplest version of periodic motion - repetitive motion back and forth through an equilibrium
if mass pulled beyond

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Page 2: Energy Conservation and Oscillation Rates

The second page delves deeper into energy conservation principles and the mathematical relationships governing oscillation rates in SHM.

Definition: Total mechanical energy in SHM remains constant in the absence of friction, alternating between potential and kinetic energy.

Highlight: At maximum displacement, velocity is zero and all energy is potential; at equilibrium, velocity is maximum and all energy is kinetic.

Example: A rotating turntable demonstration shows how circular motion projects as simple harmonic motion, where the shadow of a rotating ball appears to move back and forth.

Vocabulary: Angular frequency ωω represents the rate of oscillation in radians per second, related to frequency by ω = 2πf.

Simple Harmonic Motion: simplest version of periodic motion - repetitive motion back and forth through an equilibrium
if mass pulled beyond

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Page 3: Reference Circles and Pendulums

The final page explores the relationship between SHM and reference circles, along with practical applications in pendulum motion.

Definition: A reference circle provides a geometric interpretation of SHM, where the projection of uniform circular motion represents simple harmonic motion.

Example: A simple pendulum demonstrates SHM for small angles lessthan15°less than 15°, with its period depending only on length and gravitational acceleration.

Highlight: Real-world oscillations are typically damped due to friction, causing decreasing amplitude over time.

Quote: "Pendulum undergoes SHM for small angles where sin θ ≈ θ lessthan 15°less than ~15°"

Simple Harmonic Motion: simplest version of periodic motion - repetitive motion back and forth through an equilibrium
if mass pulled beyond

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Fundamentals of Simple Harmonic Motion

Simple harmonic motion represents the most basic form of periodic motion, characterized by repetitive movement through an equilibrium position. The motion is governed by specific parameters and mathematical relationships.

Definition: Simple harmonic motion occurs when the net force along the direction of motion follows Hooke's Law, with the force always directed toward the equilibrium point.

Vocabulary:

  • Amplitude AA: Maximum displacement from equilibrium
  • Period TT: Time taken for one complete cycle
  • Frequency ff: Number of cycles per unit time, measured in Hertz HzHz

Highlight: Hooke's Law Fs=kxFs = -kx is fundamental to understanding SHM, where k is the spring constant and x is displacement from equilibrium.

Example: A mass attached to a spring demonstrates SHM when pulled beyond its equilibrium position, oscillating between positions x = -A and x = +A.

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

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Sudenaz Ocak

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Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

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