Phase Plane 

 

Differential Equation:

Formula:

 

Set of differential equations:

Formula:

 

Finding Eigenvalues

For:

Formula:

 

Formula:

 

Formula:

Formula:

 

 

 Sub in Formula: and Formula: ,

Formula:

 

Find the determinant:

Formula:

 

Use the Quadratic Formula:

 Formula:

 

 

For Formula: and Formula:

Formula:

 

For Formula: , we get real and negative eigenvalues. If Formula: then:

Formula:

 

A check to see if Formula: is dimensionless can be found on this page.

 

For long time:

Formula:

 

 Experiments Corresponding to Equations


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