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Statistical Analysis of the Vibrating Beam

Statistical Analysis of the Vibrating Beam. THE GROUP Amanda Criner Kimberly Sacha LeVar Henderson. Project Goal. Which mathematical models can be used to describe the vibrating beam?. Outline. Collect Data Choose Model Spring Results Evaluate the Model. The Spring Model. Equation

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Statistical Analysis of the Vibrating Beam

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  1. Statistical Analysis of the Vibrating Beam THE GROUP Amanda Criner Kimberly Sacha LeVar Henderson

  2. Project Goal • Which mathematical models can be used to describe the vibrating beam?

  3. Outline • Collect Data • Choose Model • Spring • Results • Evaluate the Model

  4. The Spring Model • Equation • y’’ + Cy’ + Ky = 0 • y(0)=y0, y0’=0 • Assumptions • The beam is behaving like a spring. • The only forces are the force of the spring, friction and the voltage. • The voltage is one kick.

  5. C7=0.8630 C8=0.7010 C9=0.7753 K7=1,545 K8=1,567 K9=1,543 Data

  6. Residual vs. Fitted Value in Set 9

  7. Residual vs. Fitted Value in Set 7

  8. Residual vs. Time in Sets 7 & 8

  9. QQ Plot of Sample Data vs. Standard Normal in Sets 7-9

  10. Conclusions GOOD ENOUGH FOR US? Yes! Good introduction to modeling physical phenomena Simple enough to experiment with: Optimization algorithms Statistical analysis =Good learning tool WE AREN’T BUILDING A BRIDGE TODAY True tad!!!!

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