Optimizing a Non-Linear Oscillating Pendulum

Paul Grandstrand 2007

Hamline University

Goals

• Build a model of a non-linear oscillating pendulum

• Write a LabVIEW program to optimize the pendulum system

Linear Oscillation

€

y = c

Non-Linear Oscillation

€

y = a1xn + a2x

n−1 +...+ an−1x2 + anx+ c

Pulse Train

• A series of current pulses sent through the solenoid

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

Engineering Methods

Engineering Methods

Engineering Methods

Engineering Methods

Pendulum Bob

Pendulum Bob

Solenoid

Damper

Wiring Diagram

Wiring Diagram

Wiring Diagram

Wiring Diagram

Wiring Diagram

Array-to-Pulse-Train

Array-to-Pulse-Train

Array-to-Pulse-Train

Flipper

Array-to-Pulse-Train

Notearly

Array-to-Pulse-Train

Array-to-Pulse-Train

Optimized Pendulum

€

y = 0.002x2 − 0.02x+ 0.08

Amplitude of Generations

Final Program

Future Study

• Use my program to optimize the potential energy of oscillating nuclei in chemical bonds

Acknowledgements

• Dr. Andy Rundquist• Dr. Fred Kroeger• Hamline University• Ms. Fruen• Team Research

Optimizing a Non-Linear Oscillating Pendulum

Paul Grandstrand 2007