2007 Civic vibration when idling

I recently took my car in to have the battery checked. (I had pulled off the road into a parking lot to wait for a heavy thunderstorm to pass. While waiting, I turned off the engine, but forgot I had the headlights on. I sat there for 20 minutes. When I went to turn the car on the puny 310 cca battery was DRAINED. Had to call AAA for a jump.) At my dealership, they have a separate line for oil changes/battery checks. While they were checking the battery I pointed out how the engine was visibly vibrating. The service man found another Civic in the service line, started it and lifted the hood. Its engine shook/vibrated exactly the same way my cars engine does. I still don’t know what causes the problem, but I believe it is a flaw in the vehicle’s design. Why my car didn’t shake when it was newer I don’t know.