It sounds like your garage door may have an issue with its rollers, tracks, or possibly the springs. A shaking door can indicate that the rollers are not moving smoothly along the tracks, which can happen if dirt or debris has built up, or if the rollers themselves are worn out.
First, inspect the tracks for any obstructions or misalignment. If you notice dirt, clean the tracks with a damp cloth. You can also lubricate the rollers and tracks with a silicone-based garage door lubricant to ensure smooth operation.
If the problem persists, it might be a sign of worn-out rollers or springs that need replacing. This is especially true if the shaking occurs after the door has been idle for a while.
For safety and to ensure proper installation, I recommend hiring a licensed garage door technician to assess the situation. Typical costs for garage door repairs can range from $100 to $300, depending on the repairs needed and your location.
The next step is to get 2-3 local quotes on Handyman.com to find a qualified professional to take a look at your garage door.
— Assisted answer