Vibrating Beam Problem

Vibrating Beam ProblemVibrating Beam Problem

Three’s CompanyThree’s CompanyJeff, Russell, Dan, and ChrisJeff, Russell, Dan, and Chris

Other titlesOther titles

The George W. Bush AdministrationThe George W. Bush Administration

ASU and PalsASU and Pals

Three’s CompanyThree’s Company

Harmonic Oscillator Model 1Harmonic Oscillator Model 1

• Initial ConditionsInitial Conditions• zz00 = [d = [ddatadata(1), 0](1), 0]• cc00 = -20 = -20• kk00 = .01 = .01

• ResultsResults• Standard Error (C) = .0152Standard Error (C) = .0152• Standard Error (K) = .6004Standard Error (K) = .6004• 95% Confidence Interval (C) = (.8525, .8830)95% Confidence Interval (C) = (.8525, .8830)• 95% Confidence Interval (K) = (1550.62, 1551.82)95% Confidence Interval (K) = (1550.62, 1551.82)• Minimized Cost = 7.6843eMinimized Cost = 7.6843e-7-7

Harmonic Oscillator Model 2Harmonic Oscillator Model 2

• Initial ConditionsInitial Conditions• zz00 = [d = [ddatadata(1), (d(1), (ddatadata(2)-d(2)-ddatadata(1))/(time(2) – time(1))](1))/(time(2) – time(1))]• cc00 = -20 = -20• kk00 = .01 = .01

• ResultsResults• Standard Error (C) = .0156Standard Error (C) = .0156• Standard Error (K) = .6249Standard Error (K) = .6249• 95% Confidence Interval (C) = (.7962, .8587)95% Confidence Interval (C) = (.7962, .8587)• 95% Confidence Interval (K) = (1550.03, 1552.53)95% Confidence Interval (K) = (1550.03, 1552.53)• Minimized Cost = 7.6539eMinimized Cost = 7.6539e-7-7

Russell’s IdeaRussell’s IdeaClearly the other models did not cover Clearly the other models did not cover all data pointsall data points

Beam ModelBeam Model

• Initial ConditionsInitial Conditions• qq00 = [YI; CI; = [YI; CI; ; K; Kpp; ; pp; YI; YIpp; CI; CIpp]]

• qq0 0 = [.17060; 5.8829e= [.17060; 5.8829e-6-6; 9.2095e; 9.2095e-3-3; 3.6584e; 3.6584e--

44; .085873; .26292; 9.4044e; .085873; .26292; 9.4044e-5-5]]

• ResultsResults• q = [.17027; 6.0769eq = [.17027; 6.0769e-6-6; .0096352; 3.5897e; .0096352; 3.5897e--

44; .082879; .25496; 9.665e; .082879; .25496; 9.665e-5-5] ] • Minimized Cost = 1.0222eMinimized Cost = 1.0222e-7-7

Other things we’ve learnedOther things we’ve learnedBe aware of the connection between math, Be aware of the connection between math, the sciences, AND statistics.the sciences, AND statistics.

Word serious?Word serious?

But why?But why?

Why?Why?Cuz the world needs mathematiciansCuz the world needs mathematicians

Needs Needs mathematicianmathematician