Shaking violently

Hi, I was hoping someone could help me out. I have 2001 ford explorer sport trac 43,000Km that shakes pretty violently when the car is at stop and had the check engine light come on. Once I step on the gas everything s back to normal again. The car runs perfect except for stops, it feels like the engine is going to conk out while at rest. Also I would like to mention that I just replaced my alternator coz it was all burned out and one of my spark plugs wasnt firing(the spark plug looked brand new when t was taken out). Thanks