Coupled Oscillator: Hellie

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Problem Statement

Write up on the Wiki a solution of a coupled oscillator problem like the coupled pendulum. Use State Space methods. Describe the eigenmodes of the system. Solve Using the Matrix Exponential

 Coupled Oscillator.jpg

Initial Conditions:

F=ma

State Equations

=

With the numbers...


=


=


Eigenvalues


Eigenvectors




Standard Equation

Eigenmodes

There are two eigenmodes for the system
1) m1 and m2 oscillating together
2) m1 and m2 oscillating at exactly a half period difference


Matrix Exponential using transformation z=Tx






lots of variables

Another way to solve using the Matrix exponential



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Written by: Andrew Hellie