Statistical Analysis of the Vibrating Beam

THE GROUP

Amanda CrinerKimberly SachaLeVar 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 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.

Data

C7=0.8630

C8=0.7010

C9=0.7753

K7=1,545

K8=1,567

K9=1,543

Residual vs. Fitted Value in Set 9

Residual vs. Fitted Value in Set 7

Residual vs. Time in Sets 7 & 8

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

Conclusions

GOOD ENOUGH FOR US?Yes!

Good introduction to modeling physical phenomena

Simple enough to experiment with:Optimization algorithmsStatistical analysis

=Good learning toolWE AREN’T BUILDING A BRIDGE TODAYTrue tad!!!!