Context The needle of a sewing machine makes a repetitive up and down motion which is described by the equation y(t)=Acos(wt) To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in ? of the needle as a function of time. Constraints and information The parameter A represents the range of motion (in m); The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second; The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem; Modelization Establish the model for the y velocity of the needle as a function of time and the parameters A and w. Then test your model by calculating the speed in y of the needle at the moment and with the given parameters: Moment: 4.1 s Amplitude: 0.012 m Angular frequency: 17.9 rad/s
Context
The needle of a sewing machine makes a repetitive up and down motion which is described by the equation
y(t)=Acos(wt)
To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in ? of the needle as a function of time.
Constraints and information
The parameter A represents the range of motion (in m);
The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second;
The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem;
Modelization
Establish the model for the y velocity of the needle as a function of time and the parameters A and w.
Then test your model by calculating the speed in y of the needle at the moment and with the given parameters:
Moment: 4.1 s
Amplitude: 0.012 m
Angular frequency: 17.9 rad/s
Step by step
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