### Notes:

The Energy of a Vibrating Mass on a Spring Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

### Teaching Ideas and Suggestions:

This Concept Builder likely works best in a unit on Simple Harmonic Motion or Vibrations and Waves. And it probably works best with honors level to AP Physics 1 students. The Concept Builder focuses on how energy changes from potential to kinetic energy and back to potential energy over and over again for a vibrating mass on either a horizontal spring or a vertical spring. Students express their understanding of these changes using words (first activity), energy bar charts (second activity) and numbers (third and fourth activities). To be successful, students must understand terms kinetic energy as being due to the motion of the object, (gravitational) potential energy as being due to the height of the object, elastic potential energy as being due to the stretch and compression of a spring, and total mechanical energy being the sum of the kinetic and potential energies. We use the symbol PE consistently to represent potential energy. And when we wish to delineate between elastic and gravitational potential energy we will append a subscrip of "grav" and "spring". These notations are consistent throughout the website.

Numbers are used in the thrid and fourth activities to provide a quantitative feel for what energy conservation is. In doing so, we chose a zero level for gravitational potential energy as the height of the bottom of the spring when it is in its relaxed position. The results is that the potential energy values were negative and in most cases, the total mechanical energy turned out to be negative. This designation of the zero level should likely be discussed with students. We recognize that others may have a habit of chosing it differently (especially when doing lab work). Because of our designation, an increase in PEgrav means that the PEgrav value will become less negative.

This Concept Builder can be used as an in-class activity or (for those with Task Tracker subscriptions) as assigned homework/practice. We recommend preceeding the Concept Builder with lab work, demonstrations, and simulations (in that order). Once students have gained some comfort with the concept, allow them a chance to do the Concept Builder. There are three independent activities to complete, each of which can be quickly completed. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. Our summary of the four activities is as follows:
• KE, PE, and TME: Question Groups 1 - 6 ... Describe how the KE, PE, and TME changes as a mass vibrates on a horizontal or a vertical spring.
• Energy Bar Charts: Question Groups 7-12 ... Identify the correct energy bar charts for a mass vibrating on a horizontal spring.
• Do It With Numbers 1: Question Groups 13-18 ... Given the KE and PE values at one location for a mass vibrating on a horizontal spring, identify the KE and PE values at a second location.
• Do It With Numbers 2: Question Groups 19-24 ... Given the KE and PE values at one location for a mass vibrating on a vertical spring, identify the KE and PE values at a second location.
In order to complete an activity, a student must correctly analyze each question in that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the level (when logged in as a Task Tracker user). A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the que of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a trophy which is displayed on the Main Menu (for those students with Task Tracker accounts).

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

### Related Resources

There are a few resources at The Physics Classroom website that serve as very complementary supports for the Energy of a Vibrating Mass on a Spring Concept Builder. These include:
• Physics Interactives Simulations
One of our simulations at the Physics Interactives section may be a good complement to this activity. The Mass on a Spring simulation animates the up and down motion of a mass on a spring. The spring constant, mass value, damping and initial position can all be modified. Energy bar charts and kinematic graphs are displayed.

Visit the Mass on a Spring.

• Curriculum/Practice: If your study of pendulum motion (and vibrational motion) is a lead-in to a unit on waves, we would like to call your attention to our Curriculum Corner section with a complete set of think sheets on the topic of wave motion. If your study of pendulum energy is part of a unit on work and energy, we would like to call your attention to our Curriculum Corner section with a complete set of think sheets on the topic of energy.

Visit the Curriculum Corner - Wave Basics

Visit the Curriculum Corner - Energy

Additional resources and ideas for incorporating this Energy of a Vibrating Mass on a Spring Concept Builder into an instructional unit on Simple Harmonic Motion or Vibrations and Waves can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.