is also a linearly independent first-order dynamical invariant.

The second-order invariant of the oscillator

We may also build quadratic invariants from the equations of motion (\ref{eq:02}). Without the driving force, it would be sufficient to build linear combinations of products of these equations. However, this is not the case when the driving force is in place. Let us observe the following products between (\ref{eq:02a}) and (\ref{eq:02b}):