Coupled Oscillator: Hellie

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:

$m_{1}=10kg\,$

$m_{2}=15kg\,$

$k1=100N/m\,$

$k2=150N/m\,$

$k3=100N/m\,$

State Equations

${\begin{bmatrix}{\dot {x_{1}}}\\{\ddot {x_{1}}}\\{\dot {x_{2}}}\\{\ddot {x_{2}}}\end{bmatrix}}\,$ = ${\begin{bmatrix}0&1&0&0\\0&0&0&0\\0&0&0&1\\0&0&0&0\end{bmatrix}}{\begin{bmatrix}x_{1}\\{\dot {x}}_{1}\\x_{2}\\{\dot {x}}_{2}\end{bmatrix}}+{\begin{bmatrix}0&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&0\end{bmatrix}}{\begin{bmatrix}0\\0\\0\\0\end{bmatrix}}$

Eigenmodes

Written by: Andrew Hellie