Swinging. No, not that kind.
Destiny’s King’s Fall Raid guide – The Crux
This bit’s easy. After looting the chest from the far side of the Hall of Souls portal, run forward through the door into an area called The Crux.
You’ll see a chasm over which are swinging four huge pendulums. You have to jump across them to the door on the other side.
There’s nothing to explain here, other than to be careful of the general scale of this section. The platforms are enormous, and the relative swing can be tricky to judge.
But this really shouldn’t cause you too many problems. Jump across, run through the door and keep going forward. It doesn’t matter if you go left or right. You’ll enter a large area and run past some Hive Tomb Ships into an area called Portico.