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Optimizing a Non-Linear Oscillating Pendulum
Paul Grandstrand 2007
![Page 2: Optimizing a Non-Linear Oscillating Pendulum Paul Grandstrand 2007](https://reader035.vdocuments.site/reader035/viewer/2022062401/5a4d1b3f7f8b9ab0599a058e/html5/thumbnails/2.jpg)
Hamline University
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Goals
• Build a model of a non-linear oscillating pendulum
• Write a LabVIEW program to optimize the pendulum system
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Linear Oscillation
€
y = c
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Non-Linear Oscillation
€
y = a1xn + a2x
n−1 +...+ an−1x2 + anx+ c
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Pulse Train
• A series of current pulses sent through the solenoid
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Genetic Algorithm
• Used to optimize pulse train• Randomly generated first generation of
pulse trains• Selected pulse trains that gave greatest
amplitude and modified them to form next generation
• This next generation was then used in the next iteration of the algorithm
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Engineering Methods
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Engineering Methods
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Engineering Methods
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Engineering Methods
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Pendulum Bob
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Pendulum Bob
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Solenoid
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Damper
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Wiring Diagram
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Wiring Diagram
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Wiring Diagram
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Wiring Diagram
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Wiring Diagram
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Array-to-Pulse-Train
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Array-to-Pulse-Train
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Array-to-Pulse-Train
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Flipper
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Array-to-Pulse-Train
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Notearly
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Array-to-Pulse-Train
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Array-to-Pulse-Train
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Optimized Pendulum
€
y = 0.002x2 − 0.02x+ 0.08
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Amplitude of Generations
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Final Program
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Future Study
• Use my program to optimize the potential energy of oscillating nuclei in chemical bonds
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Acknowledgements
• Dr. Andy Rundquist• Dr. Fred Kroeger• Hamline University• Ms. Fruen• Team Research
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Optimizing a Non-Linear Oscillating Pendulum
Paul Grandstrand 2007