Problem #7: Wind Turbine Control System Monitor As a control-systems monitor, you must monitor parts of the turbine -the sensors, blades, and so on – to ensure everything is working properly. One of the wind turbines you monitor is in Toronto at Exhibition Place. This turbine is 94 m tall and has three blades that are connected to the top of the turbine (see the diagram to the right). Each blade measures 24 m in length, and they turn at a frequency of 25 revolutions per minute. a) Use a sinusoidal function to model the height above the ground, h(t), of one of the blade tips as a function of time t minutes. Assume that a cycle begins when one of the blades is at its lowest point.
Problem #7: Wind Turbine Control System Monitor As a control-systems monitor, you must monitor parts of the turbine -the sensors, blades, and so on – to ensure everything is working properly. One of the wind turbines you monitor is in Toronto at Exhibition Place. This turbine is 94 m tall and has three blades that are connected to the top of the turbine (see the diagram to the right). Each blade measures 24 m in length, and they turn at a frequency of 25 revolutions per minute. a) Use a sinusoidal function to model the height above the ground, h(t), of one of the blade tips as a function of time t minutes. Assume that a cycle begins when one of the blades is at its lowest point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) Create a sketch of this turbine over four cycles.
c) When the tip of a blade reaches 100 m in height above the ground, the sensor is activated. How many
times will a sensor from one tip be activated during one revolution?
Show your work using a sketch and explain, OR you can use algebra and show all of your work.
Transcribed Image Text:40.docx
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Problem #7: Wind Turbine Control System Monitor
As a control-systems monitor, you must monitor parts of the turbine - the sensors, blades, and so on - to
ensure everything is working properly. One of the wind turbines you monitor is in Toronto at Exhibition Place.
This turbine is 94 m tall and has three blades that are connected to the top of the turbine (see the diagram to
the right). Each blade measures 24 m in length, and they turn at a frequency of 25 revolutions per minute.
a) Use a sinusoidal function to model the height above the ground, h(t), of one
of the blade tips as a function of time t minutes. Assume that a cycle begins
when one of the blades is at its lowest point.
b) Create a sketch of this turbine over four cycles.
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