User:Egm6321.f10.team4.Yoon/Mtg26

=EGM6321 - Principles of Engineering Analysis 1, Fall 2010=

[[media: 2010_10_19_14_56_03.djvu | Mtg 26:]] Tue, 19 Oct 10

= Note on particle motion with air resistance =

[[media: 2010_09_16_14_59_27.djvu | Page 26-1]]
Note:

Particle motion with air resistance:

End Note

= Application: Euler L2-ODE-VC =

[[media: Egm6321.f09.mtg16.djvu | F09 Mtg 16]]: Higher-order derivative:

[[media: 2010_10_19_14_56_03.djvu | Page 26-2]]
Back to [[media: 2010_10_14_14_56_10.djvu | Eqn.(4)p.25-3]] (Euler L2-ODE-VC): Use [[media: 2010_10_14_14_56_10.djvu | Eqn.(1)&(2) p.25-4]] in [[media: 2010_10_14_14_56_10.djvu | Eqn.(4) p.25-3]] to obtain


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$$  \displaystyle y_{tt}-3y_t+2y=0 $$     (2)
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Stage2: Trial Solution $$\displaystyle e^{rt} $$


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$$  \displaystyle y = e^{rt} $$      (3)
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Use (3) in (2) $$\displaystyle \Rightarrow $$ characteristic equation for r(=root)

[[media: 2010_10_19_14_56_03.djvu | Page 26-3]]
Now we consider a special class of 3rd order ODEs.

= Application: Euler L3-ODE-VC =

Consider the following L3-ODE-VC:

Method 2: