General Physics 1 Module 12: Damped and Driven Oscillation PDF

Senior High School General Physics 1 Module 12: Damped and Driven Oscillation AIRs - LM LU_General Physics 1_Module12  STEM – GENERAL PHYSICS 1 Module 12: Projectile and Circular Motion Second Edition, 2021 Copyright © 20...

Senior High School General Physics 1 Module 12: Damped and Driven Oscillation AIRs - LM LU_General Physics 1_Module12  STEM – GENERAL PHYSICS 1 Module 12: Projectile and Circular Motion Second Edition, 2021 Copyright © 2021 La Union Schools Division Region I All rights reserved. No part of this module may be reproduced in any form without written permission from the copyright owners. Development Team of the Module Author: Chris Jan Cachero Nonan Editor: SDO La Union, Learning Resource Quality Assurance Team Content Reviewer: Nancy Hoggang Language Reviewer: Virgil Samonte Illustrator: Ernesto F. Ramos Jr. Design and Layout: Jhunel L. Nevado Abelaine Joy B. Abaquita Management Team: Atty. Donato D. Balderas Jr. Schools Division Superintendent Vivian Luz S. Pagatpatan, PhD Assistant Schools Division Superintendent German E. Flora, PhD, CID Chief Virgilio C. Boado, PhD, EPS in Charge of LRMS Belen C. Aquino, PhD, EPS in Charge of English Michael Jason D. Morales, PDO II Claire P. Toluyen, Librarian II Printed in the Philippines by: _________________________ Department of Education – SDO La Union Office Address: Flores St. Catbangen, San Fernando City, La Union Telefax: 072 – 205 – 0046 Email Address: [email protected] LU_General Physics 1_Module12  Senior High School General Physics 1 Module 12: Damped and Driven Oscillation LU_General Physics 1_Module12 Introductory Message This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson. Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you. Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these. In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning. Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task. If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Thank you. LU_General Physics 1_Module12  Target We are living in a world of waves; we are surrounded by waves: from simple water waves to radio waves and electromagnetic waves. We are constantly living in a world of waves, wherein we can’t live without it. We see the beauty of the world because of light waves and we can hear it becauseof sound waves. It is impossible to imagine information technology without the use of radio waves and microwaves. In this Chapter we will unravel more about the World of Waves, how it started, its kinds and its properties. After going through this Learning Material, you are expected to: 1. Differentiate underdamped, overdamped, and critically damped motion (STEM_GP12PMIId-28) 2. Define mechanical wave, longitudinal wave, transverse wave, periodic wave, and sinusoidal wave. (STEM_GP12PMIId-31) 3. From a given sinusoidal wave function infer the speed, wavelength, frequency, period, direction, and wave number (STEM_GP12PMIId-32) 4. Apply the inverse-square relation between the intensity of waves and the distance from the source. (STEM_GP12MWSIIe- 34) 1 LU_General Physics 1_Module12  Jumpstart Contentment is the Equilibrium between the enjoyment of life now and the anticipation of what is to come. -Priscilla Shirer What I know Answer the following question, write your answer on your answer sheet. 1. What is the duration of time of one cycle in a repeating motion? A. Amplitude B. Frequency C. Period D. Wavelength 2. The unit use in frequency in honor of its discoverer. A. Hertz B. Radians C. Meter D. Seconds 3. Which of the following types of waves do particles move perpendicular to the direction of the wave? A. Longitudinal B. Mechanical C. Sinusoidal D. Transverse 4. Which of the following states of matter is best for Mechanical Wave topropagate? A. gas B. plasma C. liquid D. solid 5. It is the number of cycles in a specific amount of time. A. Amplitude B. Period C. Frequency D. Wavelength What I Observed Describe the Amplitude of the pendulum as shown in the picture. __________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ __________________ 2 LU_General Physics 1_Module12  Discover LESSON 1 SIMPLE HARMONIC OSCILATION Oscillatory Motion “Oscillatory motion is the repeated to and from movement of a system from its equilibrium position. Every system at rest is in its equilibrium position. At this point, no external force is acting on it. Therefore, the net force acting on the system is zero. Now, if this system is displaced a little from its fixed point, a force acts on the system which tries to bring back the system to its fixed point. This force is the restoring force, and it gives rise to oscillations or vibrations.” Photo Credits to toppr.com Damping is the decrease in amplitude of an oscillation because of energybeing drained from the system to overcome frictional or other resistive forces. Undamped oscillations are those oscillatory motion whose amplitude remains the same or constant. It is shown in the illustration that the pendulum swings at a constant amplitude. Photo credits to Quex Book Therefore, the motion of the pendulum in wave form would look like this Photo credits to Quex Book 3 LU_General Physics 1_Module12  Damped oscillations are those oscillatory motion whose amplitude decreases with time until they achieve a state of equilibrium. In the diagram, the pendulum swings to position 1 first, then 2, 3, 4 until it becomes still (5) Photo credits to Quex Book The under damped condition in which damping of an oscillator causes it to return to equilibrium with the amplitude gradually decreasing to zero; the system returns to equilibrium faster but overshoots and crosses the equilibrium position one or more times Photo credits to Quex Book The critically damped condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position. Photo credits to Quex Book The over damped condition in which damping of an oscillator causes it to return to equilibrium without oscillating; the oscillator moves more slowly toward equilibrium than in the critically damped system. Photo credits to Quex Book 4 LU_General Physics 1_Module12  LESSON 2 CLASSIFICATION OF WAVES Waves Mechanical Electromagnetic Waves Waves Transverse Longitudi Water Radio Waves Wave nal Wave Microwaves Waves Infrared Light Ultraviolet X-ray Gamma Rays A wave is a disturbance in a medium that carries energy without particles being moved. It may take the form of elastic deformation, a variation of pressure, electric or magnetic intensity, electric potential, or temperature. Mechanical Waves Mechanical waves are defined as waves which need any type of medium for propagation. It is a wave that is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium to transport their energy from one location to another. A sound wave is an example of a mechanical wave. 5 LU_General Physics 1_Module12  Examples of Mechanical Wave  Slinky waves  Water waves  Stadium waves  Jump rope waves   Classifications of Mechanical Wave  Longitudinal waves  Transverse waves Longitudinal wave A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Longitudinal waves are always characterized by particle motion being parallel to wave motion. Examples of Longitudinal Wave  Sound waves  Tsunami waves  Earthquake  P - waves  Ultrasounds  Vibrations in gas  Oscillations in spring  Internal water waves and  Waves in slink Transverse wave A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Examples of Transverse Wave  Light wave  Audience wave  Radio waves  Television waves  Visible light waves  Ultraviolet waves  Vibrating guitar strings  Magnetic waves 6 LU_General Physics 1_Module12  SINUSOIDAL WAVE AND SINUSOIDAL LESSON 3 EQUATION Photo credits to allaboutcircuits.com A Sine wave is any oscillation, such as a sound wave or alternating current, whose waveform is that of a sine curve. A waveform that represents periodic oscillations in which the amplitude of displacement at each point is proportional to the sine of the phase angle of the displacement and that is visualized as a sine curve. Sinusoidal Equation y(x,t)=Asin(kx−ωt+ϕ) x = space coordinate t = time coordinate ϕ = phase shift k= wave number A = sine wave’s amplitude ω = angular frequency (2𝜋𝑓) Photo credits to Quex Book 7 LU_General Physics 1_Module12 Characteristics of A sine wave Cycle: In a sine wave, it is the complete event starting with a rise from zero energy to a maximum amplitude, its return to zero, the rise to a maximum in the opposite direction, and then its return to zero. Photo credits to Quex Book Frequency: The number of cycles of vibration in each unit of time. The number of cycles in a second is one Hertz (Hz), after the German physicist who discovered it. Therefore, 1Hz equals one cycle per second. 1 𝑓= 𝑇 f = frequency T = period Period: the time it takes to complete one cycle. 1 𝑇= 𝑓 f = frequency T = period Wavelength: The distance sound travels during one period, regardless of frequency. 𝑣 𝜆= 𝑓 𝜆 = wavelength v = speed f = frequency 8 LU_General Physics 1_Module12 Wave Speed: the speed at which a wave It is related to wavelength, frequency, and period by the equation: 𝑣 = 𝑓𝑥𝜆 or 𝑣 = 1 𝑥𝜆 𝑇 Where: v = speed f = frequency 𝜆 = wavelength T = period Direction of a wave: For a moving wave, you consider a particular part of it as moving. This means that the same y would be found at other x for other t, and if you change t, you need to change x in the equation of sinusoidal wave, if t increases, x must increase to make up for it. That makes a wave moves in positive direction. Wave number: refers to the number of complete wave cycles of an electromagnetic field (EM field) that exist in one meter (1 m) of linear space. Wave number is expressed in reciprocal meters (m-1). 2𝜋 𝑘= 𝜆 Speed of waves in a stretched string: The speed of waves in a stretched string depends on the tension F in the string as well as the mass per unit length μ of the string as Sample Problem 1 A 120-cm guitar string is under a tension of 400N. The mass of the string is 0.480 grams. Calculate (a) the mass per unit length of the string and (b) the speed of waves in it. Given: m = 0.480 g convert to kg l = 120 cm convert to m F = 400 N v =? 𝑚 𝐹 Formula: 𝜇= 𝑣=√ 𝑙 𝜇 𝑚 𝐹 Solution: 𝜇= 𝑣=√ 𝑙 𝜇 0.48×10−3𝑘𝑔 𝑣=√ 400 𝜇= 1.2 𝑚 −4𝑘𝑔/𝑚 4 × 10 𝜇 = 4 × 10−4𝑘𝑔/𝑚 𝑣 = 1000𝑚/𝑠 9 LU_General Physics 1_Module12 Sample Problem 2 A 120-cm guitar string is under a tension of 400N. The mass of the string is 0.480 grams. The amplitude of the wave is 0.1 m, and the angular frequency is 100 radians/s Calculate the transmitted power. Given: m = 0.480 g l = 120 cm F = 400 N A = 0.1 m ω = 100 radians/s Formula: 1 𝑃= 𝜇𝜔2𝐴2𝑣 2 Solution: 1 𝑃 = 𝜇𝜔2 𝐴2𝑣 2 −4 2 1 𝑃 = (4 𝑥10 𝑘𝑔/𝑚) ( 100 𝑚)(1000𝑚/𝑠) 2 10 LU_General Physics 1_Module12  Explore What have I learned? Lesson 1 (Damped Ways to Learn) Differentiate underdamped, overdamped, and critically damped oscillatory motion. Lesson 2 (Making Waves) Define the following classifications of waves. Mechanical Waves Transverse Waves VS Longitudinal Waves Lesson 3 (What Makes Waves) Define the different characteristics of waves discussed in Lesson 3 11 LU_General Physics 1_Module12  Exemplary Good Fair Poor Scor Criteria 5 4 3 2 e Written Written Written response Response lacks response response addresses any addresses addresses essay 1. Content essay Comprehension essay question acceptably acceptably of the essay very question very question very question. satisfactorily satisfactorily. satisfactorily. Response Response lacks Response Response is lacks any any lacks any unfocused, 2. Clarity comprehensio comprehension comprehensio illogical or n of the essay of the essay n of the essay incoherent question. question. question. Response is Response is Response is fairly Response is well organized organized and 3. organized and disorganized and developed developed with Organizatio developed, and with general n and presenting underdeveloped appropriate supporting Developmen generalization , providing little support to ideas provided t of Ideas s without or no relevant make meaning (reasons/genera adequate support. clear. l examples). support Response is 4. Grammar Response has Response has free Response has 3 , Usage and 4- 4- from any or less errors. Mechanics 5 errors. 5 errors. errors. Total Score 12 LU_General Physics 1_Module12  Deepen To deepen your understanding regarding Underdamped, Overdamped and Critically Damp Systems. Cite for technology, gadget or machine that uses Oscillatory systems to function. Waves have different characteristics, to understand these characteristics; draw a module of Sine Wave and Label the characteristics. 13 LU_General Physics 1_Module12 Problem 1 A person lying on an air mattress in the ocean rises and falls through one complete cycle every five seconds. The crests of the wave causing the motion are 20.0 m apart. Determine (a) the frequency and (b) the speed of the wave. You will be graded using the rubrics on the next page. 14 LU_General Physics 1_Module12  Rubrics for the essay Exemplary Good Fair Poor Criteria Score 5 4 3 2 Written Written Written response Response lacks response response addresses any addresses addresses essay 1. Content essay Comprehension essay question acceptably acceptably of the essay very question very question very question. satisfactorily satisfactorily. satisfactorily. Response Response lacks Response Response is lacks any any lacks any unfocused, 2. Clarity comprehension comprehension comprehension illogical or of the essay of the essay of the essay incoherent question. question. question. Response is Response is Response is fairly Response is well organized organized and 3. organized and disorganized and developed developed with Organization developed, and with general and presenting underdeveloped, appropriate supporting ideas Development generalizations providing little support to provided of Ideas without or no relevant make meaning (reasons/general adequate support. clear. examples). support Response is 4. Grammar Response has Response has free Response has 3 , Usage and 4- 4- from any or less errors. Mechanics 5 errors. 5 errors. errors. Total Score 15 LU_General Physics 1_Module12  Rubrics for Problem Solving Criteria & 5 4 3 2 1 Rating Strategic Approach Valid approach Valid Invalid Little or no Approach (S) chosen is with minor approach with approach that understanding clearly shown, errors that don’t multiple demonstrates of how to clearly written disrupt errors that little approach the & all elements understanding. impede understanding problem. are valid. understanding of the problem.. Physics Appropriate Appropriate Appropriate At least one Little or no Concepts (P) concepts that concepts that concepts concept understanding are fully are mostly identified, but identified but of physics understood understood but not employed unable to concepts. (symmetries, employed with or understood. demonstrate conserved errors. understanding. quantities, etc.), clearly stated & employed correctly. Mathematical Correct starting Correct starting Correct Can identify at Incorrect Concepts (M) equations; All equations. All starting least one equations: mathematical mathematical equations. The equation, but demonstrates steps are clearly steps are clearly mathematical unable to apply little or no shown, and shown but steps are hard them. understanding they flow easily minor errors to follow and of toward the yield wrong errors begin to mathematical correct answer. answer. impede concepts application. involved. Answer (A) 100% correct Correct answer Incorrect Unable to reach No answer. answer – analytically (IA), answer, but a correct analytically (IA) but not on the right answer on this numerically (If numerically (IA). path. path. any) & conceptually (IA). 16 LU_General Physics 1_Module12  Gauge Part 1 Multiple Choice Answer the following question, write your answer on your answer sheet. 1. What is the duration of time of one cycle in a repeating motion? A. Amplitude B. Frequency B. Period D. Wavelength 2. The unit use in frequency in honor to its discoverer. A. Hertz B. Meters C. Radians D. Seconds 3. Which of the following types of waves do particles move perpendicular to the direction of the wave? A. Longitudinal B. Mechanical C. Sinusoidal D. Transverse 4. Which of the following states of matter is best for Mechanical Wave topropagate? A. gas C. liquid C. plasma D. solid 5. It is the number of cycles in a specific amount of time. A. Longitudinal B. Mechanical C. Sinusoidal D. Transverse 6. What type of wave is produced when the particles of medium vibrate to and from in the same direction of energy transport? A. Longitudinal B. Mechanical C. Sinusoidal D. Transverse 7. When the particles of a medium are vibrating at right angles to the direction of energy transport, then the wave is a wave. A. Longitudinal B. Mechanical C. Sinusoidal D. Transverse 8. What is the amplitude of the wave in the diagram below? A. 0.03 m. B. 0.04 m. C. 0.05 m. D. 0.06 m. 17 LU_General Physics 1_Module12  9. The wavelength of the wave in the diagram above (Question #8) is m. A. 0.03 m. B. 0.04 m. C. 0.05 m. D. 0.06 m. Consider the following diagram 10. How many complete waves are shown in the diagram? A. 1 B. 2 C. 3 D. 1.5 Part 2 The linear density of the A string on a violin is 7.8 × 10-4 kg/m. A wave on the stringhas a frequency of 440 Hz and a wavelength of 65 cm. What is the tension in the string? 18 LU_General Physics 1_Module12 Answer Key 19 LU_General Physics 1_Module12 References Published Gil Nonato C. Santos, Ph.D., 2017, General Physics 1, Philippines, Rex Book Store pp. 56-73 Angelina A. Silverio, 2007, Exploring Life through Science PHYSICS Philippines, Phoenix Publishing House, pp. 53-56 Websites Oscillatory Motion: Definition, Displacement, Difference, Examples, Videos. (2020, May 19). Retrieved October 21, 2020, from https://www.toppr.com/guides/physics/oscillations/periodic- and-oscillatory- motion/ Wave - Types of Waves, Properties of Waves & Application of Waves: BYJU'S. Retrieved October 21, 2020, from https://byjus.com/physics/waves/ 20 LU_General Physics 1_Module12  For inquiries or feedback, please write or call: Department of Education – SDO La Union Curriculum Implementation Division Learning Resource Management Section Flores St. Catbangen, San Fernando City La Union 2500 Telephone: (072) 607 - 8127 Telefax: (072) 205 - 0046 Email Address: [email protected] [email protected] 21 LU_General Physics 1_Module12