This year's final should be a really good one.
It will emphasize oscillators.

For the problem involving a coupled oscillator system.
you will want to understand how to get x(t) from an initial
condition (displacement or velocity), as well as how to
calculate the normal mode freqencies and eigenvectors.

For any spinning oscillator (or wire) problem it is also
essential to understand how to get x(t) from initial conditions.

There will be a driven oscillator problem.
The important thing there is to understand what integrals are zero,
and, even more important, the relationships between the driving frequencies
and the oscillator response curve.  Also the phase shift, delta.

There will also probably be some sort of orbit problem and
maybe a mass sliding on a table....

Sarah's tilted table problem is, I think, probably pretty much
impossible to solve.  Ny guess is that it is chaotic ( hmmm...).
It illustrates an interesting point though. that most problems are pretty tough
to do anything with (in closed form); so emphasize the ones that are possible
in your preparation.  Nothing too fancy or exotic...

(PS.  You must understand eigenvectors!!)