bezier warp expression - slowing amplitude and velocity with fast decay

I've been working with an expression from Dan Ebberts Vibrating strings which I have modified to create a bending effect on a solid shape

This part is applied to a slider expression of the solid

veloc = 14;
amplitude = -250;
decay = 4;
amplitude*Math.sin(veloc*time)/Math.exp(decay*time)

Then a bezier warp has been applied to the solid shape to the Bottom Right Tangent and Bottom Left Tangent

value + [0,effect("Slider Control").param("Slider")]

This works very well except that I would like to be able to have the amplitude of the bending shape slow down as it bends and then snap back quickly in the decay but  I'm not sure how to accomplish this.  I have tried playing with the settings that I have, but am unable to make this work.

Any help would be very much appreciated.

Ira