PA114 Waves and Quanta · Unit 1: Oscillations PA114 Waves and Quanta Unit 1: Oscillations and Oscillators (Introduction) Tipler, Chapter 14 www.astro.le.ac.uk/~rda5/PA1140.

Slides:

Advertisements

Similar presentations

Oscillations and Waves Energy Changes During Simple Harmonic Motion.

Advertisements

Foundations of Physics

Physics 101: Lecture 22 Simple Harmonic Motion

Chaper 15, Oscillation Simple Harmonic Motion (SHM)

Phy 212: General Physics II Chapter 15: Oscillations Lecture Notes.

Copyright © 2009 Pearson Education, Inc. Lecture 1 – Waves & Sound a) Simple Harmonic Motion (SHM)

Chapter 13 Oscillatory Motion.

Chapter 15 Oscillatory Motion.

Springs And pendula, and energy. Harmonic Motion Pendula and springs are examples of things that go through simple harmonic motion. Simple harmonic motion.

Unit 6 Lesson 1 Simple Harmonic Motion SHM

Motion of a mass at the end of a spring Differential equation for simple harmonic oscillation Amplitude, period, frequency and angular frequency Energetics.

Describing Periodic Motion AP Physics. Hooke’s Law.

Chapter 13 SHM? WOD are underlined. Remember Hooke’s Law F = - k Δx New Symbol: “k” Spring constant. “Stiffness” of the spring. Depends on each spring’s.

Simple Harmonic Motion

Simple Harmonic Motion

OSCILLATIONS Chapter 15. Simple Harmonic Motion (SHM) Systems.

15.1 Motion of an Object Attached to a Spring 15.1 Hooke’s law 15.2.

Periodic Motion. Definition of Terms Periodic Motion: Motion that repeats itself in a regular pattern. Periodic Motion: Motion that repeats itself in.

The Simple Pendulum A simple pendulum consists of a mass at the end of a lightweight cord. We assume that the cord does not stretch, and that its mass.

Physics 203 – College Physics I Department of Physics – The Citadel Physics 203 College Physics I Fall 2012 S. A. Yost Chapter 11 Simple Harmonic Motion.

Introduction to Simple Harmonic Motion Unit 12, Presentation 1.

Simple Harmonic Motion

Chapter 11 Vibrations and Waves.

Simple Harmonic Motion. Restoring Forces in Spring  F=-kx  This implies that when a spring is compressed or elongated, there is a force that tries to.

Chapter 15 Oscillations. Periodic motion Periodic (harmonic) motion – self-repeating motion Oscillation – periodic motion in certain direction Period.

Oscillatory motion (chapter twelve)

Simple Harmonic Motion This type of motion is the most pervasive motion in the universe. All atoms oscillate under harmonic motion. We can model this motion.

©JParkinson ALL INVOLVE SIMPLE HARMONIC MOTION.

Vibrations and Waves Hooke’s Law Elastic Potential Energy Simple Harmonic Motion.

SIMPLE HARMONIC MOTION. STARTER MAKE A LIST OF OBJECTS THAT EXPERIENCE VIBRATIONS:

Simple Harmonic Motion. Ideal Springs F Applied =kx k = spring constant x = displacement of the spring +x  pulled displacement -x  compressed displacement.

Chapter 11: Harmonic Motion

APHY201 1/30/ Simple Harmonic Motion   Periodic oscillations   Restoring Force: F = -kx   Force and acceleration are not constant  

Ball in a Bowl: F g F N F g F N  F  F Simple Harmonic Motion (SHM) Stable Equilibrium (restoring force, not constant force)

Simple Harmonic Motion Physics is phun!. a) 2.65 rad/s b) m/s 1. a) What is the angular velocity of a Simple Harmonic Oscillator with a period of.

Phys 250 Ch14 p1 Chapter 13: Periodic Motion What we already know: Elastic Potential Energy energy stored in a stretched/compressed spring Force: Hooke’s.

Vibrations and Waves Chapter 11. Most object oscillate (vibrate) because solids are elastic and they will vibrate when given an impulse Tuning forks,

Oscillations Readings: Chapter 14.

Whenever the force acting on an object is: Whenever the force acting on an object is: 1. Proportional to the displacement 2. In the opposite direction,

Chapter 11 Vibrations and Waves. Simple harmonic motion Measuring simple harmonic motion Properties of waves Wave interactions.

Simple Harmonic Motion Periodic Motion Simple periodic motion is that motion in which a body moves back and forth over a fixed path, returning to each.

PHY 101: Lecture Ideal Spring and Simple Harmonic Motion 10.2 Simple Harmonic Motion and the Reference Circle 10.3 Energy and Simple Harmonic Motion.

Physics 141Mechanics Lecture 21 Oscillation Yongli Gao You may not know it, but every atom/molecule in your body is oscillating. For any system, there's.

Any regular vibrations or oscillations that repeat the same movement on either side of the equilibrium position and are a result of a restoring force Simple.

Simple Harmonic Motion (SHM). Simple Harmonic Motion – Vibration about an equilibrium position in which a restoring force is proportional to displacement.

S H M a n d W a v e s B a s i c s. T h e O s c i l l a t o r When displaced from its vertical equilibrium position, this plastic ruler oscillates back.

Chapter 10 Waves and Vibrations Simple Harmonic Motion SHM.

Simple Harmonic Motion (SHM)

Chapter 14 Periodic Motion © 2016 Pearson Education Inc.

Waves and Quanta PA114 Unit 1: Oscillations and Oscillators

Simple Harmonic Motion

Chapter 13: Oscillatory Motion

Foundations of Physics

Simple Harmonic Motion

Applications of SHM and Energy

Oscillations An Introduction.

Chapter 5.2 Notes Potential Energy.

PHYS 1441 – Section 004 Lecture #22

Oscillatory Motion.

Oscillations Readings: Chapter 14.

The Simple Pendulum A simple pendulum consists of a mass at the end of a lightweight cord. We assume that the cord does not stretch, and that its mass.

PHY138 – Waves, Lecture 2 “Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” - Richard Feynman, Nobel Laureate.

Simple Harmonic Motion

PENDULUM ©JParkinson.

PENDULUM ©JParkinson.

Group Work Predict the motion of a mass acted on only by a Hooke’s law spring. Express your prediction as a position-time graph. Explain why you believe.

Chapter 15 Oscillations.

Foundations of Physics

Ch. 12 Waves pgs

Simple Harmonic Motion and Wave Interactions

Presentation transcript:

PA114 Waves and Quanta · Unit 1: Oscillations PA114 Waves and Quanta Unit 1: Oscillations and Oscillators (Introduction) Tipler, Chapter 14 Dr Richard Alexander (G44B)

PA114 Waves and Quanta · Unit 1: Oscillations Mass on a spring Pendulum Atomic bond Oscillators Quartz crystal Tuning fork Tuning circuit

PA114 Waves and Quanta · Unit 1: Oscillations Introductory lecture - Simple harmonic motion (SHM) - Angular frequency, phase, and amplitude - Energy in SHM - Damping, forcing - Resonance

PA114 Waves and Quanta · Unit 1: Oscillations E x 0 h Anharmonic oscillator U = mgh Total Energy E = K + U

PA114 Waves and Quanta · Unit 1: Oscillations Restoring force: Whether the spring is stretched or compressed, the restoring force acts towards the equilibrium position and is linearly related to the displacement (Hooke's Law): Simple Harmonic Motion 0 x > 0 x < 0 x-direction Displacement spring constant Harmonic oscillator

PA114 Waves and Quanta · Unit 1: Oscillations T

T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

PA114 Waves and Quanta · Unit 1: Oscillations T

Newton’s 2nd Law: Solution: Parameters: A - unconstrained,  - unconstrained

PA114 Waves and Quanta · Unit 1: Oscillations Displacement Initial phase Phase SHM and circular motion

PA114 Waves and Quanta · Unit 1: Oscillations What is the energy in the system? Energy is put into the system by the initial compression or stretching of the spring (work done = potential energy) The system also has kinetic energy associated with the motion of the mass

PA114 Waves and Quanta · Unit 1: Oscillations K.E. = 1/2 mv 2 E x P.E. = 1/2 kx 2 T.E. = 1/2 kA 2 A 0 stretch compress

PA114 Waves and Quanta · Unit 1: Oscillations E x P.E. = 1/2 kx 2 T.E. = 1/2 kA 2 A 0 stretch compress Period the sameVelocities lower

PA114 Waves and Quanta · Unit 1: Oscillations Physics is about looking for patterns

PA114 Waves and Quanta · Unit 1: Oscillations Mass on a spring Pendulum Atomic bond Oscillators Quartz crystal Tuning fork Tuning circuit

PA114 Waves and Quanta · Unit 1: Oscillations Oscillators store energy - like a battery or reservoir Oscillators measure time - unlike a battery or reservoir

PA114 Waves and Quanta · Unit 1: Oscillations T.E. explains temperature, thermal expansion, melting,...

PA114 Waves and Quanta · Unit 1: Oscillations Damped SHM v friction frictional force: -v damping constant

PA114 Waves and Quanta · Unit 1: Oscillations Damped SHM

PA114 Waves and Quanta · Unit 1: Oscillations Forced, damped SHM: Resonance

PA114 Waves and Quanta · Unit 1: Oscillations Tidal resonance Forced, damped SHM: Resonance

PA114 Waves and Quanta · Unit 1: Oscillations Orbital resonance Forced, damped SHM: Resonance

PA114 Waves and Quanta · Unit 1: Oscillations Forced, damped SHM driving frequency Oscillations at driving frequency,  ; amplitude depends on how close  is to  0.

PA114 Waves and Quanta · Unit 1: Oscillations

Coupled oscillators