Dorottya Lendvai dorcinomorci@gmail.com Berzse zsenyi yi Dni - PowerPoint PPT Presentation

Dorottya Lendvai dorcinomorci@gmail.com Berzse zsenyi yi Dáni niel el Gimnázi zium, um, Budapest dapest Márton Czövek czovek.marton@gmail.com Budapest dapest Uni niver ersity sity of Techolo ology gy and nd Economics nomics Márton Vavrik Berzsenyi Dániel Gimnázium, Budapest

PENDULUM WAVE AND THE EXPERIMENTAL EQUIPMENT  a series of pendulums in an optional number  the length of each pendulum is chosen by an appropriate mathematical relation  the pendulums can shape special formations 2

THE PHYSICAL BACKGROUND : The whole pendulum wave shall return to its starting position in a short period of time. During this time each pendulum swings with different frequency. For example: during the whole period time of the pendulum wave the longest swings 52 times ► the second shall swing 53 ► then 54 and so on .  We number the pendulums: i = 0,1,2,3, … n .  The pendulum wave consists of n + 1 no. pendulums.  Pendulum no. 0 is the longest. 3

THE PHYSICAL BACKGROUND  𝛖 → 𝐮𝐢𝐟 𝐱𝐢𝐩𝐦𝐟 𝐪𝐟𝐬𝐣𝐩𝐞 𝐮𝐣𝐧𝐟 𝐩𝐠 𝐮𝐢𝐟 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧 𝐱𝐛𝐰𝐟 (the shortest time within all pendulums in the pendulum wave return to the starting position at the same time)  𝐔 𝐣 → 𝐪𝐟𝐬𝐣𝐩𝐞 𝐮𝐣𝐧𝐟 𝐩𝐠 𝐮𝐢𝐟 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧 𝐨𝐩. 𝐣.  𝐎 → 𝐨𝐩. 𝐩𝐠 𝐭𝐱𝐣𝐨𝐡𝐭 𝐧𝐛𝐞𝐟 𝐜𝐳 𝐮𝐢𝐟 𝐦𝐩𝐨𝐡𝐟𝐭𝐮 𝐣 = 𝟏 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧 during the 𝝊 time 𝝊 𝑼 𝒋 = 𝐎 + 𝒋 4

PHYSICAL BACKGROUND →  according to the well-known connection and the previous formula: l 𝑕 𝜐 2 , 𝑈 = 2π ∙ g → 𝑚 𝑗 = 4𝜌 2 ∙ 𝑈 𝑗 𝑈 𝑗 = 𝑂+𝑗  in case of given 𝝊, 𝒐, 𝑶 the length of each pendulum: 𝟑 𝒉 𝝊  𝐦 𝐣 → 𝐮𝐢𝐟 𝐦𝐟𝐨𝐡𝐢𝐮 𝐩𝐠 𝐮𝐢𝐟 𝐬𝐩𝐪𝐟 𝐨𝐩. 𝐣 . 𝒎 𝒋 = 𝟓𝝆 𝟑 ∙  𝒉 → 𝐛𝐝𝐝𝐟𝐦𝐟𝐬𝐛𝐮𝐣𝐩𝐨 𝐩𝐠 𝐡𝐬𝐛𝐰𝐣𝐮𝐳 𝑶 + 𝒋 Demo data:   𝛖 = 𝟘𝟏 𝐭 → the whole period time of the pendulum wave  n = 15 → n + 1 = 𝟐𝟕 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧𝐭 / i = 0,1,2,3, … n /  N = 52 → no. of swings made by the longest pendulum From these data, the required length of the cordes can be set. 5

THE ACCOMPANYING SIMULATION  We need to know every pendulum ’s length and its current angle at any moment.  We already know the lenghts.  We can find any pendulum ’s angle-time function: 𝑕 𝛽 𝑢 = 𝛽 0 cos 𝑚 𝑢 . aswell, the requirement is to have Java Runtime Environment 7 to run:  http://berzsenyi.hu/Lendvai/  http://java.com/en/ 6

EVALUATION – NICE SHAPES 10 s (1/9 period) 15 s (1/6 period) 18 s (1/5 period) 36 s (2/5 period) 7

Pendu dulum um No. of sw swings ngs During ng 45 45 sec 45 S – HALF TIME ( 𝝊 = 𝟘𝟏 𝒕 ) no. No. of swings ngs (1/2 PERIOD) 0 52 26 1 53 26 1/2 2 54 27 3 55 27 1/2 4 56 28 5 57 28 1/2 6 58 29 7 59 29 1/2 8 60 30 9 61 30 1/2 10 62 31 11 63 31 1/2 12 64 32 Every second pendulum is at the 13 65 32 1/2 same position: the even ones are on 14 66 33 15 67 33 1/2 the starting position, the odd ones are on the opposite side. 8

Pendu dulum um No. of s swing ngs During ng 30 30 sec 30 S ( 𝝊 = 𝟘𝟏 𝒕 ) no. No. of swings ings (1/3 PERIOD) 0 52 17 1/3 1 53 17 2/3 2 54 18 3 55 18 1/3 4 56 18 2/3 5 57 19 6 58 19 1/3 7 59 19 2/3 8 60 20 9 61 20 1/3 10 62 20 2/3 11 63 21 12 64 21 1/3 There are 3 different positions 13 65 21 2/3 the pendulums can be in, 14 66 22 but only 2 is visible . 15 67 22 1/3 9

Pendu dulum um No. of s swing ngs During ng 30 30 sec 30 S ( 𝝊 = 𝟘𝟏 𝒕 ) no. No. of swings ngs (1/3 PERIOD) 0 52 17 1/3 1 53 17 2/3 2 54 18 3 55 18 1/3 4 56 18 2/3 5 57 19 6 58 19 1/3 7 59 19 2/3 8 60 20 9 61 20 1/3 10 62 20 2/3 11 63 21 12 64 21 1/3 There are 3 different positions 13 65 21 2/3 the pendulums can be in, 14 66 22 but only 2 is visible . 15 67 22 1/3 9

22,5 S (1/4 PERIOD) 10

MORE CURIOSITIES  the simulation did learn physics  „ butterflies ”  sound of pendulum wave 11

THE BUILDING AND SET-UP  stable supporting structure  procurement of the balls (or other hanging objects)  selection of ropes (not breakable, or spinning)  accurate suspension  fine tuning and syncronization (after the precise measurement)  Computer method /for example: Webcam Laboratory Program/  Manually: We swing and carefully tune the length of each pendulum by eye-measurement: extend or shorten with the small screws 12

PHYSICS SCHOOL CAMP each year four day 40-50 selected students open-air school 13

PHYSICS SCHOOL CAMP  previous preparation: project work small groups jointly chosen topic under supervision of teachers  form of the project’s framework experiment measurement evaluation theory calculation physics history building of equipment computer simulation  other programs teachers hold small groups lessons invited performers experiments thought-provoking tasks team competitions 14

LITERATURE AND SPECIAL THANKS [1] Dorottya Lendvai, Márton Czövek, Bence Forrás: Pendulum wave or love at first sight / Fizikai Szemle 2015/5, 171-177 – in Hungarian, and to be published in English [2] J. A. Flaten, K. A. Parendo, Pendulum waves: A lesson in aliasing, Am. J. Phys., 69 (7), 2001 [3] R. E. Berg, Pendulum waves: A demonstration of wave motion using pendula, Am. J. Phys., 59 (2), 1991 [4] http://www.berzsenyi.hu/Lendvai Tamás Tél Bence Forrás 15

EXCITING PENDULUM WAVES & EMERGING ISSUES  Pendulum wave with fireballs: https://www.youtube.com/watch?v=u00OF3ilNUs  Pendulum wave in the dark: https://www.youtube.com/watch?v=7_AiV12XBbI  Symmetrical pendulum wave: https://www.youtube.com/watch?v=vDtfWxL-Ajg  the length of ropes form an arithmetic series 16