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

• logy

gy and nd Economics nomics

Márton Vavrik

Berzsenyi Dániel Gimnázium, Budapest

 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

PENDULUM WAVE AND THE EXPERIMENTAL EQUIPMENT

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: 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.

THE PHYSICAL BACKGROUND

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 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)

 𝐔𝐣 → 𝐪𝐟𝐬𝐣𝐩𝐞 𝐮𝐣𝐧𝐟 𝐩𝐠 𝐮𝐢𝐟 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧 𝐨𝐩. 𝐣.

 𝐎 → 𝐨𝐩. 𝐩𝐠 𝐭𝐱𝐣𝐨𝐡𝐭 𝐧𝐛𝐞𝐟 𝐜𝐳 𝐮𝐢𝐟 𝐦𝐩𝐨𝐡𝐟𝐭𝐮 𝐣 = 𝟏 𝐪𝐟𝐨𝐞𝐯𝐦𝐯𝐧

during the 𝝊 time

THE PHYSICAL BACKGROUND

𝑼𝒋 = 𝝊 𝐎 + 𝒋

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 according to the well-known connection and the previous formula:

𝑈 = 2π ∙

l g → 𝑚𝑗 = 𝑕 4𝜌2 ∙ 𝑈𝑗 2,

𝑈𝑗 =

𝜐 𝑂+𝑗

 in case of given 𝝊, 𝒐, 𝑶 the length of each pendulum:

 𝐦𝐣 → 𝐮𝐢𝐟 𝐦𝐟𝐨𝐡𝐢𝐮 𝐩𝐠 𝐮𝐢𝐟 𝐬𝐩𝐪𝐟 𝐨𝐩. 𝐣.

 𝒉 → 𝐛𝐝𝐝𝐟𝐦𝐟𝐬𝐛𝐮𝐣𝐩𝐨 𝐩𝐠 𝐡𝐬𝐛𝐰𝐣𝐮𝐳



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.

PHYSICAL BACKGROUND →

𝒎𝒋 = 𝒉 𝟓𝝆𝟑 ∙ 𝝊 𝑶 + 𝒋

𝟑

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 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 = 𝛽0 cos

𝑕 𝑚 𝑢 .

aswell, the requirement is to have Java Runtime Environment 7 to run:

 http://berzsenyi.hu/Lendvai/  http://java.com/en/

THE ACCOMPANYING SIMULATION

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10 s (1/9 period) 15 s (1/6 period) 18 s (1/5 period) 36 s (2/5 period)

EVALUATION – NICE SHAPES

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45 S – HALF TIME (1/2 PERIOD)

Every second pendulum is at the same position: the even ones are on the starting position, the odd ones are

• n the opposite side.

Pendu dulum um no.

• No. of sw

swings ngs (𝝊 = 𝟘𝟏 𝒕) During ng 45 45 sec

• No. of swings

ngs

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 13 65 32 1/2 14 66 33 15 67 33 1/2

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30 S (1/3 PERIOD)

Pendu dulum um no.

• No. of s

swing ngs (𝝊 = 𝟘𝟏 𝒕) During ng 30 30 sec

• No. of swings

ings

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 13 65 21 2/3 14 66 22 15 67 22 1/3

There are 3 different positions the pendulums can be in, but only 2 is visible.

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30 S (1/3 PERIOD)

Pendu dulum um no.

• No. of s

swing ngs (𝝊 = 𝟘𝟏 𝒕) During ng 30 30 sec

• No. of swings

ngs

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 13 65 21 2/3 14 66 22 15 67 22 1/3

There are 3 different positions the pendulums can be in, but only 2 is visible.

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22,5 S (1/4 PERIOD)

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 the simulation did

learn physics

„butterflies”

 sound of pendulum wave

MORE CURIOSITIES

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 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

THE BUILDING AND SET-UP

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PHYSICS SCHOOL CAMP

each year four day 40-50 selected students

• pen-air school

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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

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Tamás Tél Bence Forrás [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

LITERATURE AND SPECIAL THANKS

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 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

EXCITING PENDULUM WAVES & EMERGING ISSUES

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