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Vibrating Beam Problem

In this study, Jeff, Russell, Dan, and Chris tackle the Vibrating Beam Problem using harmonic oscillator models. By analyzing initial conditions for two distinct models, we derive standard errors and construct 95% confidence intervals for critical parameters. The results highlight the importance of accurate data coverage and the interrelation between mathematics, sciences, and statistics. Key findings include minimized costs and noteworthy distinctions between models. The work emphasizes the imperative for skilled mathematicians to comprehend and resolve complex real-world problems.

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Vibrating Beam Problem

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  1. Vibrating Beam Problem Three’s Company Jeff, Russell, Dan, and Chris

  2. Other titles • The George W. Bush Administration • ASU and Pals • Three’s Company

  3. Harmonic Oscillator Model 1 • Initial Conditions • z0 = [ddata(1), 0] • c0 = -20 • k0 = .01 • Results • Standard Error (C) = .0152 • Standard Error (K) = .6004 • 95% Confidence Interval (C) = (.8525, .8830) • 95% Confidence Interval (K) = (1550.62, 1551.82) • Minimized Cost = 7.6843e-7

  4. Harmonic Oscillator Model 2 • Initial Conditions • z0 = [ddata(1), (ddata(2)-ddata(1))/(time(2) – time(1))] • c0 = -20 • k0 = .01 • Results • Standard Error (C) = .0156 • Standard Error (K) = .6249 • 95% Confidence Interval (C) = (.7962, .8587) • 95% Confidence Interval (K) = (1550.03, 1552.53) • Minimized Cost = 7.6539e-7

  5. Russell’s Idea • Clearly the other models did not cover all data points

  6. Beam Model • Initial Conditions • q0 = [YI; CI; g; Kp; rp; YIp; CIp] • q0 = [.17060; 5.8829e-6; 9.2095e-3; 3.6584e-4; .085873; .26292; 9.4044e-5] • Results • q = [.17027; 6.0769e-6; .0096352; 3.5897e-4; .082879; .25496; 9.665e-5] • Minimized Cost = 1.0222e-7

  7. Other things we’ve learned • Be aware of the connection between math, the sciences, AND statistics. Word serious? But why?

  8. Why? • Cuz the world needs mathematicians Needs mathematician

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