2014 Fu Lan Physics Festival Physics Experimental Exploration Competition

In the first semester of my freshman year, I gathered my classmates and formed a small undergraduate research group. I then led the research group to complete in the “15th Fu Lan Physics Festival Scientific and Cultural Exchanges of University Students Across the Taiwan Strait Physics Experimental Exploration Competition”. I was very honored that our group won the “Best Design Award” given by Sun Yat-san University in China.

國立清華大學教務處教學發展中心讀書會成果報告 學期別: 103學年度第一學期 讀書會編號: 10310G099 讀書會名稱: 舞動的鎖鏈---分析串珠下落的運動 小組成員(學號): 李依哲102022193, 謝承翰103022192, 黃聖耀103022208, 徐筠婷103022143, 劉玥伶102022161, 陳慶豐103020091, 陳艾霖103022138 中華民國 一百零三 年 十二月 十二日 Table of Contents:

• Purpose and Visions

• Members:

• Main Project:Abstract Introduction Method Data Analysis Conclusion Further Development

• Presentation

• Awards

• Purpose and Missions:

In this study group, we aimed at focusing on the development of research abilities of the group members. Our vision is to encourage university freshmen and develop their passion in science by letting university freshman to work together to solve a real life question. In the process they will learn more about how to communicate and present their work as well. The overall mission is to present the research work on chain fountain in “15th Fu Lan Physics Festival Scientific and Cultural Exchanges of University Students Across the Taiwan Strait Physics Experimental Exploration Competition”. The overall preparation time is less than 2 months, which is very challenging for university freshmen.

• Members:

Our study group consists of 7 members. 6 freshmen, and 1 second year undergraduate. Most of us joined the university in September, and it was amazing for us to produce such work within 2 months.

• Main Project:Abstract: When the chain fountain reached the steady state, in theory the curve region can be approximate by circular motion. However, when observed carefully, observable disturbances can be found across the string even at steady state. This paper provides an interesting findings on the pattern of the disturbances waves in the steady state chain function. Introduction:

Chain fountain is a surprising questions for many physicist, as string mechanics had been well studied centuries ago. Papers on the dynamics of chain fountain had been produced only recently. However, the small disturbances on the chain fountain, is often ignored in these papers. It is because in theory, when the steady state is reached, the small disturbances of the wave would be cancelled out completely. It’s due to its superposition with its own reflection from the ground. When we tested out experimentally, the small disturbances on the chain fountain exists at all time. This results motivate us to doubt the existence of a steady state, and to find the wave composition of the small disturbances. In the following section, we will test the hypothesis of steady state, provide full details of experimental approach to analyze wave composition of small disturbances and our findings.

• Overview of the experiment:

Video analysis approach is taken to obtain quantitative data on the small disturbances of the wave. A high speed camera is used to record the motion of beads chain. A frame with closest circular shape on the curved section of the chain fountain is set as reference frame. Then in each frame the position of the beads is marked using a program called “Tracker”. Then interpolation approach is taken. First, by fixing the y values, the x direction displacement can be found. Then same approach is repeated for the y-direction. The data is then input for Discrete Fortier Transformation and then the frequency formation of the small disturbance can be found.

• Apparatus:

• 1 High Speed Camera 50fps

• 1 Bead Chain with beads’ diameter 4mm

• 1 Cup with height of 12.3 cm

• 3 Stroboscope (50Hz)

• 1 Squared Paper

• 1 Bubble level

• 3 Black Foam Boards

• Tapes

Figure 1: Experimental Setup

• Method:Fixed the black foam board on table with tapes. Setup the high speed camera and change the setting so the fsp is 50 Hz. Setup the stereoscope, so the light flashes to the beads in 3 different angles. (Note: The camera can see 2 bright spots on each beads, because of 2 rays of light reflected to the camera.) Use bubble level to level the camera and table. Use squared paper to test whether or not spherical aberrations exists when filming. Place the Bead chain and cup on the table for the camera to focus. Start recording the video and release the beads chain at the same time. Repeat Step 1 ~ 6 until the motion of the chain recorded is perfectly sideway to the camera. (This prevents geometric mapping in 3 dimensions.)

• Data Analysis:

First, the video is cut into 115 frames. Each frame is presented as a picture, and the time interval between each frame is seconds. In each frame the beads appears as 2 parallel lines. This is due to the 2 bright spots on each beads moving with a speed. In order to test whether or not steady states exists, LabVIEW computer software is used to analyze the speed of each beads.

Figure 2: The sample beads’ velocity in steady state

Figure 2 shows that the velocity of the beads is nearly constant, therefore steady states do exist.Tracker software is then used to locate each position of the beads in the 36 frames after the reference frame. There are more than 4000 beads are located manually.

Figure 3: Image of beads locating process The frame is then compared with the reference frame.

Figure 4: Beads location comparison in 2 different frame Then by using interpolation approach is taken to produce displacement in x-axis.

Figure 5: Displacement Curve over time of 5 sample points​​

The data is then input for Discrete Fortier Transformation and then the frequency formation of the small disturbance can be found.

Figure 6: The Frequency formation of the small disturbance The frequency of the peaks are then plotting over the order it occurs.

Figure 7: The order of the peaks vs. Frequency

• Conclusion:

The experimental results shows some interesting findings. First, the small disturbances in the steady state is not random and have a certain frequency composition. Second, the beads chain have larger disturbance for certain frequency, and the frequency is similar to the standing wave on a string with 2 fixed ends. Third important conclusion is that, the frequency formation of the disturbance is independent of how the bead chain is placed initial, and it is only a characteristic of the bead chain. Therefore, each bead chain have its characteristic frequency formation.

• Further Development

The further development of this experiment is to develop a theory to explain why the disturbance behave in such manner. It would be challenging and interesting to determine the equation linking the chain’s properties and the small disturbances.

• Presentation:

We are honorable to represent National Tsing Hua University to present our research findings in 15th Fu Lan Physics Festival Scientific and Cultural Exchanges of University Students Across the Taiwan Strait Physics Experimental Exploration Competition. In these 2 months, we spent huge amount of time discussing papers and experimenting. Here are our pictures of our presentation in Sun Yat-Sen University, Guangzhou, China.

Also our performance of the play “Romeo and Juliet” is greatly successful and entertained all the audiences. We also sightseeing around the city and visited many historical places.

• Awards:

It is an honor for us to won the prize for the best design in the physics experimental exploration competition.