Physical interpretation for system of ODE

[Bruno Tolentino]

If an ODE of 2nd order like this A y''(x) + B y'(x) + C y(x) = 0 has how physical/electrical interpretation a RLC circuit, so, how is the electrical interpretation of a system of ODE of 1nd and 2nd order?

<br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> \alpha_{11} &amp; \alpha_{12} \\ <br /> \alpha_{21} &amp; \alpha_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}
<br /> \begin{bmatrix}<br /> A_{11} &amp; A_{12} \\ <br /> A_{21} &amp; A_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d^2 x}{dt^2}\\ <br /> \frac{d^2 y}{dt^2}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> B_{11} &amp; B_{12} \\ <br /> B_{21} &amp; B_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> C_{11} &amp; C_{12} \\ <br /> C_{21} &amp; C_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> 0\\ <br /> 0<br /> \end{bmatrix}

 

[Simon Bridge]

Can you interpret systems of DEs in terms of mixing in tanks?

 

[HomogenousCow]

Could it be a system of two damped oscillators coupled to each other?