# Physical interpretation for system of ODE

1. Sep 25, 2015

### 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?

$$\begin{bmatrix} \frac{d x}{dt}\\ \frac{d y}{dt} \end{bmatrix} = \begin{bmatrix} \alpha_{11} & \alpha_{12} \\ \alpha_{21} & \alpha_{22} \end{bmatrix} \begin{bmatrix} x\\ y \end{bmatrix}$$
$$\begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix} \begin{bmatrix} \frac{d^2 x}{dt^2}\\ \frac{d^2 y}{dt^2} \end{bmatrix} + \begin{bmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{bmatrix} \begin{bmatrix} \frac{d x}{dt}\\ \frac{d y}{dt} \end{bmatrix} + \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix} \begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix}$$

2. Sep 26, 2015

### Simon Bridge

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

3. Sep 26, 2015

### HomogenousCow

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