Diagnosis
This is normal for the stock stand. It has a single, narrow neck and a relatively small footprint, offering minimal stability for the large 34-inch panel.
How to Fix It
The permanent solution is to replace the stand. The monitor uses a standard 100x100mm VESA mount pattern. Purchase a third-party monitor arm or sturdy VESA stand. Attach the VESA plate directly to the monitor's rear mounting point, bypassing the Samsung stand entirely.
If That Didn't Work
For a temporary fix, ensure the stand is fully clicked into the monitor. Then, add weight to the stand's base. Adhesive lead tape or a small, dense weight placed centrally on the base can lower the center of gravity and reduce wobble.
Heads Up
When attaching a VESA arm, you must first remove the Samsung stand's mounting bracket from the monitor. This requires pressing a release latch on the bracket where it connects to the monitor neck. Do not force it.