Vibrational Motion - Complete Toolkit

Objectives

1. To identify several examples of vibrating objects and to use terms such as equilibrium position, restoring force, fixed end, and damping to describe their motion.
2. To describe an object undergoing periodic motion using terms such as sinusoidal, cycle, period, amplitude, and damping and to relate these terms to the position-time graph.
3. To define period, frequency, and amplitude and to determine their values from verbal and graphical descriptions of a vibrating object's motion.
4. To describe and explain the motion of a simple pendulum using such representations as a free-body diagrams, position-time graphs, velocity-time graphs, energy tables, equations for period, and terms such as position, velocity, and acceleration.
5. To describe and explain the motion of a vibrating mass on a spring using such representations as a free-body diagrams, position-time graphs, velocity-time graphs, energy tables, energy bar charts, equations for period, and terms such as position, velocity, and acceleration.

 

Readings from The Physics Classroom Tutorial

1. The Physics Classroom Tutorial, Waves Chapter, Lesson 0

 

Interactive Simulations

1. Physics Interactive: Mass on a Spring
   
   This simulation from The Physics Classroom's Physics Interactives section animates the vibrational motion of a mass on a spring. The position-time and velocity-time graph of the motion are represented in real-time. Bar charts showing the kinetic energy, gravitational potential energy, and elastic potential energy are also shown in real-time. Users can alter the mass that is hung on the spring, the stiffness of the spring, and the amount of damping. Two springs are included for conducting side-by-side comparative studies. This variable-rich environment allows students to explore a variety of relationships related to vibrating masses on springs. The Physics Classroom has prepred a ready-to-use exercise that focuses on the question of what variables affect the period and the frequency of the vibrating mass.
   
   
   
    
2. PhET:  Hooke’s Law Simulation
   
   As 17^th-century physicist Robert Hook determined, “As the extension, so the force.” This newer HTML5 simulation lets students stretch and compress springs to explore the relationships among force, spring constant, displacement, and potential energy. It will help them gain insight into the meaning of “restoring force” an area of documented student misconception. It also promotes understanding of the predictable mathematical relationships that underlie Hooke’s Law. Teachers: The simulation can be set up as a spring system in either series or parallel. In addition, click the “Energy” tab to explore how potential energy stored in the spring changes with spring constant (k) and displacement. 
   
   
   
    
3. PhET:  Pendulum Lab
   
   This simulation displays one or two pendulums to explore how the period of a simple pendulum depends on the length of the string, mass of the pendulum bob, and amplitude of the swing. Use the Photogate timer to easily measure the period! You can vary the friction or jump to Planet X to explore the effect of changing gravity on a pendulum. Teachers: You will want to check out the PhET “Gold Star” teacher-submitted activities for great lesson plans to accompany this simulation. 
   
   
   
    
4. Hooke’s Law Digital Lab
   
   This two-hour digital lab for high school physics was created specifically to accompany the PhET simulation “Masses and Springs”. In the first lesson, students explore how displacement of a spring is mathematically related to the load applied to it. In the next day’s exploration, learners analyze the energy of a mass oscillating on a spring by observing distribution and transfer of kinetic, potential, and gravitational potential energy. Turn-Key Resource: includes explicit directions for use of the simulation, problem sets, rubric, and answer key. 

 

Video and Animations

 

Labs and Investigations

Problem-Based Learning Activity: Real-World Applications

 

Interactive Digital Homework Problems

 

Classroom Learning Module: Understanding Periodic Motion

 

Problem-Solving Exercises:

1. The Calculator Pad, Wave Basics, Problems #1-4
   
   Link: http://www.physicsclassroom.com/calcpad/waves/problems

 

 

Science Reasoning Activities:

1. The Period of a Pendulum
    
2. Mass on a Spring
   
   Link: http://www.physicsclassroom.com/reasoning/waves

 

Historical Context:

1. The Story Behind the Science:  Pendulum Motion
   
   Bet you’ve never heard of this wonderful collection of 30 science stories developed to help students explore key science concepts through the eyes of the real people who were involved. This “Story” explores the humble pendulum and its significant role in the development of modern science. Inspired by Galileo’s classic experimentation, the pendulum provided the Western world’s first accurate means of timekeeping. But perhaps more importantly, the story of the pendulum brings to light the shift to the use of mathematics to understand the natural world – the methodological core of the Scientific Revolution. It also delves into the value of idealization in science. 
    

 

 

Common Misconception:

1. Confusion of Amplitude and Period
   
   A vibrating object tends to lose energy over the course of time. This is referred to as damping. Damping causes the amplitude of vibration to decrease from one cycle to the next cycle. Students observing this will often use the phrase "slowing down" to describe the decrease in amplitude. They may even suggest that the period is decreasing. Such statements need to be corrected for a variety of reasons. First, the vibrating object is constant increasing and decreasing its speed from cycle to cycle. The increases in speed occur as the object is approaching its equilibrium position and these increases defy any description of the object "slowing down." Second, the tendency to confuse a decrease in amplitude with a decrease in period demonstrates a huge confusion on the student's part. The period of vibration remains constant from cycle to cycle; damping doesn't alter the period of vibration. 

 


 

 

Standards:

A. Next Generation Science Standards (NGSS)
 

• When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models.
• Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. 

• The total amount of energy and matter in closed systems is conserved.
• The transfer of energy can be tracked as energy flows through a system.

• Develop and use a model based on evidence to illustrate the relationships between systems or between components of a system.

• Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design: decide on types, how much, and accuracy of data needed to produce reliable measurements and consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly.

• Analyze data using tools, technologies, and/or models (e.g. computational, mathematical) in order to make valid and reliable scientific claims.

• Create or revise a simulation of a phenomenon, designed device, process, or system.
• Use mathematical models and/or computer simulations to predict the effects of a design solution on systems and/or the interactions between systems.

• Construct an explanation based on valid and reliable evidence obtained from a variety of sources (including students' own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future.
• Apply scientific reasoning to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion.

• Communicate scientific and technical information (e.g. about the process of development and the design and performance of a proposed process or system) in multiple formats (including orally, graphically, textually, and mathematically).