University of Florida/Egm4313/s12.team11.imponenti/R5.5

R5.6

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solved by Luca Imponenti

Problem Statement

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Complete the solution to the following problem

 

where

 

and

 

Find the overall solution   corresponds to the initial condition:

 
Plot the solution over 3 periods.

Taking the derivatives of the particular solution  

Particular Solution

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Plugging these into the ODE yields

     

Equating like terms allows us to solve for M and N

 

 

 

 

 

So the particular solution is

 

Overall Solution

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The overall solution in the sum of the homogeneous and particular solutions

 

 

To find A and B we apply the initial conditions

 

 

Taking the derivative

 

 

 

 

Giving us the overall solution

    

Plot

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The period for   is  

Plotting the solution   over 3 periods yields

 

Egm4313.s12.team11.imponenti (talk) 01:56, 30 March 2012 (UTC)