Basically this "Inertial Dampening" systems works like a magnet falling though a cooper pipe https://youtu.be/5BeFoz3Ypo4
But replace the falling magnet with a crew capsule surrounded by a powerful electromagnet with a magnetic field reflective material in-between. And replace the cooper pipe with a long elevator shaft which is also insulated on the outside with a magnetic field reflective material to prevent damage to outside electronics.
Basically, when the ship is doing a high g burn the crew capsule will be in a very slow freefall down the long elevator shaft like a magnet through a copper pipe.