Pendulum Waves

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What is Pendulum Wave

What is Pendulum Wave

• Many different period pendulums consist of Pendulum Waves.

• The length of each pendulum and gravity determine the period of each pendulum.

• By varying the length of a series of pendulums, some very interesting patterns emerge.

Outline

• Method• Environment• Result• Future Work

Method

• …• :a “Pendulum Wave” period• N:the times of longest pendulum oscillates, the

second to longest pendulum oscillates N+1 times• d:The interval distance between each two

adjacent pendulums• x:the total distance (from beginning to the end)• We use L(x) to design our length of each pendulum

Method

• According to L(x) equation and our parameter,we have got the result below.

Pendulum 01 02 03 04 05 06

Length 9.85 1.04 1.1 1.16 1.23 1.31

Pendulum 07 08 09 10 11 12

Length 1.39 1.48 1.58 1.69 1.81 1.95

Method

• After setting the length of each pendulum and other parameters. We have to simulate how these pendulums wave.

• We have to know it’s wave function.• The wave displacement function can be

written as

Method

• The wave displacement function can be written as

• :angular frequency, owing to the difference of pendulum length, we can combined it with[1] then we inferred

• k: Wave number k at the very beginning of the oscillation.

• A:amplitude of the waves• Finally,

Environment

• Textures make experiment equipment more authentic.(the board the lamp and the bar )

• Also lighting and material parameters make the pendulum looks more heavy , like the real ones.

• Yellow: gold • red:ruby • white:pearl • orange:copper (According to OpenGL Material)

EnvironmentAmbient Diffuse Specular

Gold 0.24725

0.1995

0.0745

0.75164

0.60648

0.22648

0.628281

0.555802

0.366065

Pearl 0.25 0.20725

0.20725 1 0.829 0.829 0.2966

480.296648

0.296648

Ruby 0.1745 0.01175

0.01175

0.61424

0.04136

0.04136

0.727811

0.626959

0.626959

Copper

0.19125 0.0735 0.0225 0.7038 0.2704

8 0.0828 0.256777

0.137622

0.086014

Environment

Result

Future Work

• We need more accurate calculation, because after the whole pendulum waves loop a few cycles, the displacement of some pendulum strayed out a little bit.

• GPU programming maybe suited to this simulation of Pendulum waves, because we can take apart these 12 pendulum waves as parallel process working simultaneously.