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Stability & Vibration Damping in Alpine Skiing – Integration Guide (Grades 7 – 12)

This document is a companion piece to video titled Stability & Vibration Damping in Alpine Skiing and is intended as a resource for educators.

Background and Planning Information

About the Video

Stability & Vibration Damping in Alpine Skiingdiscusses the methods and importance of damping vibrations in alpine skiing. Featured athletes are Iraq war veteran and Paralympian Heath Calhoun and three-time Olympic medalist Julia Mancuso, both of whom will be competing in the 2014 Winter Olympics in Sochi. Also featured are Kam Leang, Associate Professor of Mechanical Engineering and carbon nanotube expert at the University of Nevada, Reno, and Tom Watson, an off-road motorcycle engineer who helped design the shock absorption mechanism for Heath Calhoun’s mono-ski. The video points out that vibrations cause skis to intermittently lose contact with the snow surface, which results in a loss of control and speed. The carbon nanotube technology, which is incorporated into the construction of skis, and the fluid-based shock absorber in Calhoun’s mono-ski both allow enhanced damping of vibrations and therefore more consistent contact with the snow, allowing skiers to go faster.

0:00 0:14

Series opening

0:15 0:58

Introducing Mancuso and Calhoun

0:59 1:43

Why vibrations matter to alpine skiers

1:44 2:02

Introducing Leang

2:03 3:12

Explaining how skis are constructed using nano-materials

3:13 3:34

Calhoun’s mono-ski and vibration

3:35 4:17

Introducing Watson who designs a shock absorber for Calhoun

4:18 4:52

Explaining how Calhoun’s shock absorber works

4:53 5:16


5:17 5:32

Closing credits

Language Support:

To aid those with limited English proficiency or others who need help focusing on the video, click the Transcript tab on the side of the video window, then copy and paste the text into a document for student reference.

Promote STEM with Video

Connect to Science

Science concepts described in Stability & Vibration Damping in Alpine Skiing include the idea that elements—carbon in this case—can take on different structures at the atomic level, with very different properties. Carbon has many allotropes—or different forms of the same element —including graphite, diamond, graphene, and fullerenes such as the nanotubes described in the video. Phosphorus, sulfur, oxygen, and iron are a few other examples of elements with different allotropes.

Related Science Concepts

  • allotropy

(page 1)

  • crystalline structure
  • molecular bonding
  • physical properties

Take Action with Students

  • Encourage groups of students try to name various forms of carbon and start a discussion about the familiar ones of graphite (“pencil lead”) and diamond. Students may be surprised to learn they are different forms of the same element. Have students brainstorm to think of how different arrangements of carbon atoms could yield such different properties. Have students research different uses of graphite and diamond, apart from pencils and jewelry.
  • Have students split up into groups, with each group choosing an element that has multiple allotropes. Some other elements that have allotropes are sulfur, oxygen, and phosphorous. Have students research the different properties of their chosen element’s allotropes and present their findings to the class. Student research might start here:

Connect to Technology

Carbon nanotubes have many different properties, depending on such factors as their size, the nature of the spiral pattern in the molecular structure, and whether they are single-layered or have tubes nested within other tubes. Possible uses, some of which are in practice today, include nanotube-based electronic circuits for computers and even nano-motors.

Take Action with Students

  • As a class, conduct Internet research to find some of the many possible uses of carbon nanotubes. After seeing the options, allow groups of students to choose an application for further research, collaborating outside of class. Have students report back to the class. Their presentations should focus on how such applications might affect their lives in the relatively near future.
  • Many technologies that improved people’s lives in the past were thought to be as fanciful as nano-scale technologies when first introduced. Examples include inventions such as the electric generator, the transistor, and fiber optics. Have groups of students identify a past innovation or discovery that has changed people’s lives. When each group reports back to the class their presentation should focus on how the discovery or innovation was made, how and why further development was done, how it was implemented into daily life, how long the whole process took and how their invention or innovation benefited people of the time.

Connect to Engineering Design

The engineering design process uses human ingenuity to draw from science, math, and technology to solve a problem. Carbon nanotubes can be used to create new materials with special properties of strength, thermal or electrical conductivity, and possibly even as “scaffolding” for biological applications such as growing organs. While arranging these nanotubes in specifically desired ways can be challenging, the benefits offered by nanotubes make the design and support of nanotube manufacturing systems essential.

(page 2)

Take Action with Students

  • Have students work in groups to find materials-science or biomedical applications for carbon nanotubes. Hold a mini “Engineering Fair” in the school cafeteria or atrium to highlight the importance of STEM subjects in future professions.
  • Groups of students can brainstorm and discuss how carbon nanotubes are made, and how a mixture of different tubes might be organized to produce relatively uniform batches. Have groups then research to find how carbon nanotubes are manufactured and present these findings to the class. Students’ efforts should focus on practical problems of nanotube standardization and material purity, and how engineers are currently having success in these areas.
  • Have students identify and discuss the challenges and precautions that need to be understood when working with nanotechnology. Point out that the potential impact on human health is unknown at this time.

Connect to Math

Vibrations consist of a system oscillating periodically back and forth to either side of an average state or location (equilibrium position). Although mathematical descriptions of these vibrations would be connected to an Algebra 2 curriculum and can usually be described by sine or cosine functions, they in turn have parameters such as amplitude and frequency, which are wave properties students have been exposed to since elementary school. The vibrations can be damped, so that their amplitude decreases with time. This decrease in amplitude can itself be modeled as an exponential decay, where a number (such as the natural logarithm base, called e) is raised to a negative power multiplied by the time. While this may sound complicated, it can be easily programmed into a spreadsheet such as Excel, Numbers, or Google Sheets and the results graphed automatically to show students. Then, altering parameters allows one to quickly visualize the different possibilities, ranging from gradual decay of vibrations to such rapid decay that the vibration never gets to complete even one cycle.

Take Action with Students

  • Visualize exponential decay for students by bouncing a ball once and having students observe and graph the decreasing amplitude of the successive bounces. Guide them to connect the decreasing amplitude to damping.
  • • Use an interactive whiteboard and a spreadsheet program such as Excel, Numbers or Google Sheets to mathematically model a vibration, and then a damped one. To do so, follow these steps.
    • In cell A1, type time interval and in A2 type the number 0.1. (Note: The entries in the spreadsheet should not be in italics.)
    • In A3 type time, in A4 type 0, and in A5 type =A4+$A$2. Then, copy and paste A5 all the way down through A504. To do so, highlight cell A5 and drag the cursor to A504 highlighting all cells. Then use the fill down command from the Edit menu. This will result in a list of times up through 50, going by intervals of 0.1.
    • Type the following in B1: amplitude, B2: 1, C1: frequency, C2: 1, B3: undamped, B4: =$B$2*COS($C$2*A4), and then copy B4’s contents into B5 through B504. Again, fill down. These are the values of a cosine wave with the amplitude in B2 and the angular frequency (in radians per second) in C2, at the times in column A.
    • Next, type in D1: time constant, D2: 0.1, C3: damped, C4: =B4*EXP(-$D$2*A4), and then copy C4 down through C504. Again, fill down. These are the values of the wave in column B, multiplied by a damping factor.
    • Finally, insert a chart off to the right and use Excel’s options and instructions to have it plot smooth-line scatter plots of columns B and C versus column A (starting in row 4). To do so, highlight the cells 4 through 504 in columns A, B, and C, and go to Insert: chart. Click on the X Y Scatter button and choose a smooth line. You should see a cosine wave and a damped version of it. Have students experiment with changing the values in row 2 and note the effects on the graphs. Results should look like this example from Excel.

(page 3)

Damped and Undamped Spreadsheet

Incorporate Video into Your Lesson Plan

Integrate Video in Instruction

As Part of the Day

  • Predict: Show the short segment of video from 1:32 to 1:41, where it shows a ski being vibrated. Have students select roughly ski-shaped objects from around the classroom (i.e., rulers, meter sticks, etc.) and then predict which ones’ vibrations might dampen most quickly, while giving a justification for their prediction. Then, have students hold or clamp the objects to the edge of a table and displace the end by a standard amount. Upon release, the objects will likely vibrate, damping to an imperceptible amplitude in a short time, which students measure and record. Students can then make predictions about how shortening or lengthening a ski would affect the vibrations a skier might encounter. Alternatively, multiple candidates could be released at the same time for a direct comparison of damping. Students might try altering the length free to vibrate, the amount of initial displacement, or make composite materials by taping together different objects. In each case, they should predict the effect in advance.
  • Compare and Contrast: Show the part of the video from 3:20 to 4:30, where the shock absorber for Heath Calhoun’s mono-ski is described. Have students research how the human knee functions as a shock absorber, and compare and contrast its function with that of the mono-ski. Have groups of students compare and contrast the human knee and the mono-ski to determine if the mono ski has any advantages or disadvantages relative to the knee for downhill skiing.

(page 4)

  • Homework: Have students do research to investigate examples of composite materials in everyday use. Have students find an item in their home (such as plywood used in construction or laminated countertops) that uses composite materials and bring it, or a picture of it, to school. Part of the presentation should describe what the composite material is and how it is advantageous in that particular application. Some help can be found at:

As Part of a 5E Lesson Plan

If you use a 5E approach to lesson plans, consider incorporating video in these Es:

  • Engage: Ask students about any experiences they have had in which vibrations occurred and needed damping or other means of reduction. Ask them to describe any damping mechanisms that were in place. Or, students might brainstorm to think of cases where vibrations occur deliberately and efforts are made to avoid damping them. An example might be a musical instrument, such as with guitar strings and tuning forks.
  • Elaborate: Vibrations can grow stronger if some outside influence is helping cause them in a rhythmic way, and this forcing occurs at the same frequency with which the object naturally vibrates. This phenomenon is called resonance and can be a problem or a desired effect. Have students research and then discuss the meaning of the term, and then give examples of situations where resonance is desired or needs to be damped or otherwise suppressed. As a discussion starter, use search_query=examples+of+resonance&sm=1.

Connect to ... History

Metallurgy and Military History

The video’s concentration on mixing carbon nanotubes with other materials (such as epoxy) is an example of materials science, which has ancient origins, including the history of metallurgy. Ancient (and more recent) people have found by accident, design, or trial and error that mixing different metals together or mixing in other substances (including carbon) changes the properties of metals in important and often advantageous ways. This had many implications, one of which is that an army with stronger and/or lighter swords had an advantage over its opponents. Mixing things with metals contributed to the spread of ancient empires. Have students research metallurgy in various cultures at various times. They might focus on whether such discoveries were deliberate or serendipitous, and whether they were developed independently in other parts of the world.

Connect to ... History of Science


The history of the discovery and synthesis of buckyballs, which led to the nanotechnology movement, is interesting, too. According to, the discovery of the unique structure of the C60 was published in the journal Nature and had a mixed reception— both criticism and enthusiastic acceptance. Students might start their research at that site.

(page 5)

Connect to ... Automotive Engineering

Shock Absorbers

Students experience damping of vibrations every time they ride in a car. The technology is similar to that which Tom Watson applied to Heath Calhoun’s mono-ski, but there are many other shock absorbers types as well. Have students work in groups, each choosing a different method of automotive shock absorption to research and later report on. Students might also find out and share what type is used in their car(s).

Connect to ... Economics

The Business Cycle

Vibrations occur both in nature and in man-made systems, whenever there exists what is called a restoring force or negative feedback. The stronger these effects are, the more frequently the system oscillates between extremes. One important example of this is called the business cycle, in which boom years of strong economic growth and activity are interspersed with bust years of recessions (or depressions). Government agencies often attempt to apply damping mechanisms to discourage large swings (though perhaps not wanting to discourage growth so much). Introduce this topic by showing the class a graph (easily found online) of economic data such as unemployment or inflation rate and ask students if they see periodic vibrations, Then, have them do research on the business cycle or economic oscillations, perhaps even including the search word damping. Have them report their findings to the class.

Connect to ... Language Arts

Numerical Prefixes

The prefix nano- has come into very widespread use. According to, 233 words start with nano- in the English language. Students might first investigate what is numerically meant by nano- and by other numerical prefixes and then explain why carbon nanotubes are called this, rather than calling them microtubes or minitubes.

Use Video as a Writing Prompt

Have students use persuasive writing to convince a friend that his or her skis might be too flexible and that a new pair that damp vibrations experienced on the slopes would be money well spent. Persuasive claims could include evidence from the video as well as other resources.

Connect Video to Common Core ELA

Encourage inquiry via media research. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use prompts liberally to encourage thought and discussion.

Common Core State Standards Connections: ELA/Literacy –

  • RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions
  • WHST.6-8.1 Write arguments focused on discipline-specific content.
  • WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.
  • WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

(page 6)

Facilitate Inquiry through Media Research

Show Stability & Vibration Damping in Alpine Skiing and encourage students to jot down notes while they watch. Elicit questions and problems from group members and help them determine which are better explored using print media or online resources. Then, students should brainstorm to form a list of key words and phrases they could use in Internet search engines that might result in resources that will help them answer a question or solve a problem. Review how to safely browse the Web, how to evaluate information on the Internet for accuracy, and how to correctly cite the information found. Suggest students make note of any interesting tangents they find in their research effort for future inquiry. Encourage students with prompts such as the following:

  • Words and phrases associated with our question are....
  • The reliability of our sources was established by....
  • The science and math concepts that underpin a possible solution are....
  • Our research might feed into an engineering design solution such as....
  • To conduct the investigation safely, we will....

Related Internet Resources

Make a Claim Backed by Evidence

As students carry out their media research, ensure they record their sources and findings. Students should analyze their findings in order to state one or more claims. Encourage students with this prompt: As evidenced by... I claim... because....

Present and Compare Findings

Encourage students to prepare presentations that outline their inquiry investigations so they can compare findings with others. Students might do a Gallery Walk through the presentations and write peer reviews as would be done on published science and engineering findings. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as:

  • My findings are similar to (or different from) those of the experts in the video in that....
  • My findings are similar to (or different from) those of my classmates in that....
  • My findings are similar to (or different from) those that I found on the Internet in that....

(page 7)

Reflect on Learning

Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t before. Encourage reflection, using prompts such as the following:

  • I claim that my ideas have changed from the beginning of this lesson because of....
  • My ideas changed in the following ways....
  • When thinking about the claims made by the experts, I am confused about....
  • One part of the investigation I am most proud of is....

Inquiry Assessment

Assessment Rubric for Inquiry Investigations


1 point

2 points

3 points

Initial question or problem

Question or problem had had a yes/no answer or too simple of a solution, was off topic, or otherwise was not researchable or testable.

Question or problem was researchable or testable but too broad or not answerable by the chosen investigation.

Question or problem was clearly stated, was researchable or testable, and showed direct relationship to investigation.

References cited

Group incorrectly cited all of the references used in the study.

Group correctly cited some of the references used in the study.

Group correctly cited all of the references used in the study.


No claim was made or the claim had no evidence to support it.

Claim was marginally supported by the group’s research evidence.

Claim was well supported by the group’s research evidence.


Groups neither effectively nor cooperatively presented findings to support their stance.

Groups effectively or cooperatively presented findings to support their stance.

Groups effectively and cooperatively presented findings to support their stance.

Findings comparison

Only a few members of the group constructively argued their stance.

Most members of the group constructively argued their stance.

All members of the group constructively argued their stance.


None of the reflections were related to the initial questions.

Some reflections were related to the initial questions.

All reflections were related to the initial questions.

Sports in this article

Alpine Skiing