Coupled Oscillator: horizontal Mass-Spring

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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 and eigenvectors of the system.

 Horizontal spring.jpg

Initial Conditions:

Equations for M_1

Equations for M_2

Additional Equations

State Equations

=

With the numbers...


=

Eigen Values

Once you have your equations of equilibrium in matrix form you can plug them into a calculator or a computer program that will give you the eigen values automatically. This saves you a lot of hand work. Here's what you should come up with for this particular problem given these initial conditions.

Given

We now have

From this we get