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.
Initial Conditions:
![{\displaystyle m_{1}=15kg\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe9c531ae3332079b8839fbfe4f369129d3cc52b)
![{\displaystyle m_{2}=15kg\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/530caa27e8d91f217807e90e212f6c383db43ccc)
![{\displaystyle k1=100N/m\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4b17f71550f5aeb090d99c8f9c8aedf68d45d79)
![{\displaystyle k2=150N/m\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4a7c157042420bca0b6a57a8e4ea09fe8e8e4bf)
![{\displaystyle k3=100N/m\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4ce8a753cec11c6ed4dca2621c3fe1df72f5f7f)
State Equations
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With the numbers...
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Eigenmodes
- There are three eigenmodes for the system
- 1) m1 and m2 oscillating together
- 2) m1 and m2 oscillating at exactly a half period difference
- 3) m1 and m2 oscillating at different times
Solve Using the Matrix Exponential
Written by: Andrew Hellie