Is there a way to make align orientation and position contraints bouncy?

Hello there! Since a bunch of time, iv’e been trying to make good looking and stable suspensions for my train, and for that i am now using align position and orientation constraints. The problem with those is that their way to operate is just to directly to the goal with a ‘Sine’ style movement, but to make it look realistic, it should go a bit more over its goal, and then go to the goal, in a ‘Back’ Style.

Here are some videos to explain my idea better:

Current suspension : https://gyazo.com/01c200e3045d8467db18d55b9ac2359f

Wanted ‘Style’ : MP59 : Voyage entre Mairie des Lilas et Place des Fêtes sur la ligne 11 du métro parisien - YouTube

In conclusion i would need it to be moving constantly and make the motion more natural.

Try using spring constraints. If done right then it will work a lot better.