 E2.22
 AP2.2
 E3.15
 P3.3
 P3.10
 DP3.1
 DP3.3
 MP3.5
Homework 2, due September 12, 2007

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Homework 2, due September 12, 2007
All problems are from the 10th edition of the course text.
Bill Goodwine, 376 Fitzpatrick
question on DP3.3
On DP3.3, the equations are nonlinear with respect to x1 due to the angle the cable makes as it is pulled away from x1=0. Are we supposed to solve the equations numerically and guess values of Kd until it meets the given criteria or is there something I'm missing that will allow us to solve these nonlinear equations such that we can find Kd analyitically? Thanks.

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Re: question on DP3.3
I haven't worked it out fully myself, but I'm pretty sure what happens is that the nonlinearity due to the angle that the force is applied to the airplane from the cables is canceled by a corresponding nonlinearity in the amount that the spring is stretched. I think if you fully work out m \ddot x = forces, while some nonlinearities show up in the forces, they eventually cancel.bmertz wrote:On DP3.3, the equations are nonlinear with respect to x1 due to the angle the cable makes as it is pulled away from x1=0. Are we supposed to solve the equations numerically and guess values of Kd until it meets the given criteria or is there something I'm missing that will allow us to solve these nonlinear equations such that we can find Kd analyitically? Thanks.
Bill Goodwine, 376 Fitzpatrick
Re: question on DP3.3
I can't get the nonlinearities to cancle out. There are two that are causing me problems
1: the hypotinuse length sqrt(h^2 + x[1]^2)
2: x[1] x[2] / hypotinuse from the angle
should we attempt to numerically solve these nonlinear equations or
should we try to solve this by linearizing the hypotinuse length? A problem with linearizing the hypotinuse is that it is not a good approximation for all x[1] values from 0  30. Any recommendations on dealing with this?
1: the hypotinuse length sqrt(h^2 + x[1]^2)
2: x[1] x[2] / hypotinuse from the angle
should we attempt to numerically solve these nonlinear equations or
should we try to solve this by linearizing the hypotinuse length? A problem with linearizing the hypotinuse is that it is not a good approximation for all x[1] values from 0  30. Any recommendations on dealing with this?

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Re: question on DP3.3
Linearizing really isn't an option since, if I recall correctly, the angle of the cable goes from 0 to 45 degrees. If necessary, you may resort to numerics.jmengers wrote:I can't get the nonlinearities to cancle out. There are two that are causing me problems
1: the hypotinuse length sqrt(h^2 + x[1]^2)
2: x[1] x[2] / hypotinuse from the angle
should we attempt to numerically solve these nonlinear equations or
should we try to solve this by linearizing the hypotinuse length? A problem with linearizing the hypotinuse is that it is not a good approximation for all x[1] values from 0  30. Any recommendations on dealing with this?
Bill Goodwine, 376 Fitzpatrick
State variable representation for RLC
Dr. Goodwine,
I think this is the correct statevariable representation of the RLC circuit we did in class:
Sorry it took so long; I forgot my controls notebook this morning and had to rework it.
I think this is the correct statevariable representation of the RLC circuit we did in class:
Sorry it took so long; I forgot my controls notebook this morning and had to rework it.