Jack-in-the-Box

This is a variation on the pendulum expression.

Keyframes were applied to Jack's position at frames 0 and 1 to move him out of the box

After Effects 6.5
Useful things
Expressions

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Then this expression was applied to the position property to give him the bouncy motion:

veloc = 35; 
amplitude = 30; 
decay = 1.0; 
y = amplitude*Math.cos(veloc*time)/Math.exp(decay*time);
value + [0,y]

Adjust the velocity, amplitude and decay parameters as needed.

(Min. Version: After Effects 6.5, Category: Useful things, Type: Expressions)

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