For many teachers, the topic of vibrational motion is a stand-alone topic, often placed in the Mechanics section of the coure. For others, vibrational motion is a segue into the study of mechanical waves. Wherever it is placed, the topic of period and frequency are usually included as a part of the study. This Concept Builder can be an effective formative assessment tool to assist students in assimilate the concept and frequency and period into their understanding of a vibrating object.

This Concept Builder can be used as an in-class activity or (for those with Task Tracker subscriptions) as assigned homework/practice. After some discussion, demonstrations, lab work, and practice with the distinction between frequency and period, allow students to put the principles into practice by the completion of the exercise. The Concept Builder includes three unique and independent activities. 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 three activities is as follows:

• Basic Concepts: Question Groups 1 - 6 ... Identify the definition, unit, mathematical meaning, and variables affecting the frequency and period of a vibrating mass on a spring.
• Ranking Tasks: Question Groups 7-9 ... Given values of mass, spring constant, and spring length for three trials, rank the trials in order of their frequency or their period. 
• Proportional Reasoning: Question Groups 10-15 ... Use proportional reasoning skills to predict the quantitative effect of changes in mass and the spring constant upon the frequency and period of a vibrating mass on a spring.

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. 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). This system of stars and trophies allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

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. 

 

 

There are a few resources at The Physics Classroom website that serve as very complementary supports for the The Period and Frequency of a Vibrating Mass on a Spring Concept Builder. These include:

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