#spring-mass

So before jumping into details of stability of solutions to ODEs, let's take another example of phase plot.

As we have already studied in our elementary physics course the vibration of simple undamped mass-linear spring system is

$$ m\ddot{x}+kx=0$$

So the state of this system is

$$ \left( \begin{array}{c} \dot{x} \\\ \dot{v} \end{array} \right) = \left( \begin{array}{c} v \\\ -\omega^2 x \end{array} \right) $$

And using maple we plot the phase plot -