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You can use pretty much any movie editor that allows the import of single frames. First line up your audio, work out where you want the key frames to be (eg for reversing the movement when shaking the head) and then fill in the other frames. If your editor allows interpolation between frames, then you can use this to make the movie less jerky. Or you can ...
There's a tutorial on how to make a bouncing ball karaoke-style lyric follower using After Effects here: http://aescripts.com/beat-assistant/ The example you give should be simpler, as the ball only bounces on each quarter-note beat -there aren't any lyrics to worry about.
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