University of Florida/Egm4313/s12.team11.gooding/R2/2.1

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Problem R2.1


Part 1[edit]


Problem Statement[edit]


Given the two roots and the initial conditions:




Find the non-homogeneous L2-ODE-CC in standard form and the solution in terms of the initial conditions and the general excitation .
Consider no excitation:

Plot the solution

Solution[edit]


Characteristic Equation:[edit]




 


Non-Homogeneous L2-ODE-CC[edit]


 

Homogeneous Solution:[edit]




Since there is no excitation,

 

Substituting the given initial conditions:[edit]



 


 

Solving these two equations for and yields:

 

Final Solution[edit]


 

2.1fig1.jpg

Part 2[edit]


Problem Statement[edit]


Generate 3 non-standard (and non-homogeneous) L2-ODE-CC that admit the 2 values in (3a) p.3-7 as the 2 roots of the corresponding characteristic equation.

Solutions[edit]



 



 



 


--Egm4313.s12.team11.gooding 02:01, 7 February 2012 (UTC)