I started to ponder following problem. I have a driven, damped oscillator where the mass is free to vibrate in y-direction. If I put a wall or a ground near the mass, the mass touches it if the drive amplitude is larger than the distance to the ground. How does this change the normal dynamics. I would expect that the oscillation becomes pretty complex depending on forcing amplitude and spring parameters. Is it possible to derive the amplitude equation for given frequency and spring parameters?