What is the important response quantity you want to get out of the simulation?

For example, say the top plate has a mass and an initial velocity. During the simulation, you can monitor the acceleration of the top plate, which starts at zero, reaches a peak and then goes down as the top plate velocity comes to zero.  Peak acceleration is a good response quantity.  Distance to reach zero velocity is another good response quantity. But these two responses might need a different mesh quality to achieve convergence.  The acceleration response might need some filtering of the data to remove high frequency ringing, whereas the displacement response probably won't need any filtering.