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Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?

Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?
Transcribed Image Text:Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?
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