How do I program a Yoshi Flutter Jump

I and a friend are trying to program the player of our game to have a Yoshi-esque flutter jump. So it would be like a double jump but on the second jump it turns into a slow hover that build up propulsion, like he's fighting to stay in the air. We where trying to make it from pure code but we honestly don't know where to start. We've messed around with gravity setting but nothings coming out right. We would love to hear some ideas that would point us in the right direction.

here's a link of what we are trying to achive.

Use sine behaviour. When second jump is trigger set Y position determined by sine movement for few second then disable the jump function. Just raw explanation from me, maybe I will make an example for your case.

EDIT

here I create flutter jump example

Thanks! That works great! I'm barely getting into Sine behavior, can't wait to experiment with the capx.

Oh well good to hear that from you. Valuable experience for me to figure out how this unique jump works.